A spokeswoman for Galveston's largest hospital system says it is prepared to provide emergency care as needed.
"We are prepared to see patients and we are gearing up to do that at this time," Chris Comer, vice president of public affairs for the University of Texas Medical Branch at Galveston, to FOXNews.com at just after 1 p.m. Central time.
And city emergency responders have warned the hospital that many residents will need treatment.
"We've heard that it is a serious situation," she said. "Emergency responders are fighting fires and there are many residents who are trapped."
Comer said all of the hospital's patients, more than 200, were evacuated ahead of the storm.
So far, three people from a single family are the only ones being treated in the hospital's emergency center. The hospital is currently seeking a transfer for that family to a hospital that was not affected by Hurricane Ike.
Five hundred staff members remain on the hospital's campus.
"We needed to keep the folks here who can keep the core operations going as we are the major healthcare provider for this area and need to be ready to respond to any medical emergencies," she said.
The hospital is operating on emergency power and has had "some wind and water damage," Comer said.
"And communications are still spotty at this time," she said.
She said the hospital is not able to admit patients to the hospital.
"Our goal is to treat and transfer," she said, adding that many patients will bypass UT Galveston and be taken directly to hospitals in San Antonio and other cities outside of Hurricane Ike's path.
On Friday, hurricane trackers warned Galveston residents that those remaining on the island in one- or two-story homes faced certain death. Still, about 40 percent — almost 25,000 — of Galveston's 58,000 residents chose to stay behind.
Mary Jo Nashcke, speaking from Galveston's emergency operations center to FOX News at about 11:15 a.m. Central time, said many residents who chose to stay behind did so because of negative experiences they had with Hurricane Rita in 2005.
"It took upwards of 40 hours to make a six-hour drive (during Hurricane Rita)," she said. "Those who did not heed the warning just did not feel it was as important to do as we were stressing.
"In the immediate future, we need to assess who is still in homes and stranded in water and who needs medical attention," she added.
Alison Castle, press secretary for Texas Gov. Rick Perry, said Galveston is under 2-4 feet of water and emergency responders would be using air, land and boats to residents.
"We don't know what we are going to find," Galveston Mayor Lyda Ann Thomas said. "We hope we will find the people who are left here alive and well."
Dr. Manny Alvarez, managing editor for FOXNewshealth.com, said many of the residents who remained in Galveston may still need to be evacuated in coming days because of "unsanitary conditions" triggered by the hurricane, especially since many homes are without running water and toilet facilities.
In Clear Lake, Texas, about 30 miles from Galveston, Disaster Officer Jana Sweeny told FOXNews.com Saturday it was a "rough" night and her description of the current situation was bleak.
She said residents of Galveston and surrounding areas who stayed behind began checking into the Hilton Hotel — where Sweeney was stationed — Friday afternoon, with pets in tow. The hotel's power was knocked out overnight and the plumbing failed. Sweeney said toilets were no longer flushing. Some flooding occurred in the lower level of the hotel and some windows were damaged by the winds.
She said the hotel is doing the best it can under the circumstances, putting bottled water into the hallway for residents, but it's not a shelter and can only do so much.
"This is really a lesson as to what happens when people don't evacuate to an emergency shelter when they're told to do so," she said.
She was awaiting information from Galveston officials, and estimates on how many people will need help.
"We hope people planned ahead," she said. "We know that with Gustav, power was knocked out even in shelters for a week."
Elsewhere in Texas, one Houston hospital said it was without power but still able to care for patients.
"We are safe, and operating under our own power," Gale Smith, a spokeswoman for The Methodist Hospital System in Houston, told FOXNews.com Saturday morning.
There were some minor leaks around the building, she added, and a few windows popped open, "but, overall, things look good here at Methodist."
The hospital has about 700 patients in residence.
Methodist Hospital has also set up a pet shelter and daycare facility for the use of essential personnel.
Canright said the hospital also housed 95 inmates from Texas Department of Criminal Justice, and they were evacuated to a facility in Tyler, which is north of Galveston.
Since the hospital has switched from paper files to electronic files, it is much easier to transfer a patient’s medical records during the hurricane evacuation, Canright said.
An evacuee from Hurricane Ike gave birth in the bathroom of a shelter Saturday in New Braunfels, Texas with the help of an expert in geriatric psychiatry who delivered his first baby in two decades.
Dr. Mark Burns told the New Braunfels Herald-Zeitung in a report for Saturday's newspaper that it was kind of like riding a bicycle.
Ku Paw delivered a baby girl on the floor of the girls restroom at Church Hill Middle School in New Braunfels with the aid of Burns, intensive care nurse Peggy Bielke and a few volunteers.
Paw, an evacuee from Calhoun County along the Texas coast, was staying with about 270 others. She was evaluated at a hospital earlier but returned to the shelter with the expectation she wouldn't go into labor until Monday.
Over in Lake Charles, La., which is nearly three hours from Galveston, residents were also experiencing what Mayor Randy Roach called a "major flooding event."
Nonetheless, Christus St. Patrick Hospital still has to prepare for one of its busiest weeks ever, said Karen Stubblefield, the hospital's public information officer.
"Less than 50 percent of the community evacuated," Stubblefied said. "So the risk to hurt themselves outside is far greater. And, we will take in patients this week from hospitals who are less equipped than us. We are preparing for a really busy 48 hour to seven day operation."
In Louisiana, Ike's storm surge inundated thousands of homes and businesses. In Plaquemines Parish, near New Orleans, a sheriff's spokesman said levees were overtopped and floodwaters were higher than either hurricane Katrina or Rita.
"The storm surge we're experiencing, on both sides of the Mississippi River, is higher than anything we've seen before," Marie said.
The Associated Press contributed to this story.