The family of a missing Illinois woman is offering a $20,000 reward for information leading to her whereabouts.

Lisa Stebic, a 37-year-old mother of two, was last seen April 30 at her home in the 13200 block of Red Star Drive in the southwest suburb of Plainfield, Ill., about 20 miles west of Chicago.

Her family created a Web site, www.findlisastebic.com, to aid efforts to find her.

Stebic's relatives held a news conference Tuesday morning to officially announce the reward.

"It's hard to be optimistic after a week of no news," said Melanie Greenberg, the family spokeswoman whose husband, Mark, is a cousin of Stebic's. "We're just hoping that someone will come forward with this new reward and bring some new information to the Plainfield police.

"It's incomprehensible that she would leave her children, she just would not," she continued. "And that's the big mystery."

"We're just hopeful that somebody out there can give us a tip, give us an idea," Stebic's sister, Debbie Ruttenberg, earlier told FOX News. "Anyone who could possibly have recognized her, please come forward. We are desperate to find Lisa. Our family is totally distraught."

Stebic's family and friends say there's no way she would have left home voluntarily more than a week ago without saying a word to anyone.

"Lisa is a person who worked as a lunch lady at a local school so she could be home for her children every day after school," Greenberg said. "It's incomprehensible to us that she would have just left."

Stebic's husband, Craig, voluntarily handed over the family computer to police. Authorities still have it in their possession.

Asked whether Craig Stebic was a suspect, Plainfield Police Chief Donald Bennett told FOX News: "We have to look at all the things, but right now we're really trying to gather information, trying to put a timeline together ... as to what her whereabouts was."

But Lisa's family told FOX News that as of Tuesday, Craig had refused to take a polygraph test.

"We're just hoping that Craig will cooperate fully with the Plainfield police and whatever they need to do to bring Lisa home," Greenberg said. "We're just hoping he will change his mind and talk to them and if there's any additional information they need, he will provide it."

While Lisa's family repeatedly refused to say whether they think Craig had something to do with her disappearance, they said he had earlier indicated he would take a polygraph, so they were surprised when he decided not to.

They are hoping he will change his mind, the family said Tuesday, adding that is concerned some in the media seem to be pointing the finger at him.

"It's something he's been thinking about … he's quite concerned with the press reports and what is happening so he, at least for now, decided not to take a polygraph," said Mark Greenberg, Lisa's cousin. "We're hoping he changes his mind on that."

Craig's sister, Jill Webb, told FOX News on Tuesday that he did agree to the test over the weekend, but "under the advice of his divorce attorney … the advice was, at this point, it probably wouldn't be a good idea to do this."

Webb said her brother basically just sits in his home office by the phone, waiting for news.

"Of course he's devastated, he's in shock. I can't imagine a worse nightmare for somebody to go through," Webb said. "It's a waiting game. It's a horrible waiting game."

Craig and Lisa Stebic were in the midst of a divorce, and although they lived in the same house, they rarely spoke to each other.

"Since they hadn't spoken, I don't know if he knew a lot of what she was doing," Webb said.

Mark Greenberg encouraged anyone who has any information to come forward.

"People just don't up and disappear. There is somebody out there who knows something," he said.

On Sunday afternoon, about 60 volunteers gathered at an elementary school near Stebic's home. They fanned out to wooded areas, parks and farm fields to search for clues. They also went to subdivisions and shopping areas to distribute fliers displaying a photograph of Stebic and her description.

Craig Stebic, 41, said he was working in the backyard and their young children were out when his wife disappeared.

"I can't see her leaving her kids," Craig Stebic told the Chicago Tribune. "She's a good mother. She'd do anything for her kids."

Lisa Stebic worked out at the Plainfield North High School track every night. Her husband believes someone picked her up. She took only her purse and cell phone; her cell phone and credit cards haven't been used since April 30.

The children, who are 10 and 12, were home when Lisa returned from work that day but were not there when she vanished.

"They're very upset, I'm sure, as any child would be missing their mother," Greenberg said.

Investigators were aware of an Internet posting she made on April 11 looking for "female friends only" to join her in exercise, he said. She listed her "goals" as "increase cardio, tone up, simply get out more, meet new people, just have fun."

"I am a parent and would like to include my children in my health activities," she wrote in the posting, in which she said she was "looking for partners to get out and enjoy nature."

"She was only asking for a female friend, someone to go running with," Greenberg said. "She was making changes in her life, trying to become more physically fit. She wasn't looking for a boyfriend to go running with."

Craig Stebic said he filed for divorce after 14 years of marriage in January when his wife declared in October that she "didn't want to be married to me anymore," the Chicago Tribune reported. Since then, he said, they've lived separate lives in the same house and have not spoken more than five words to each other in five months.

"From what we can gather, it was a relationship that was strained," Bennett told FOX News on Monday. "She would come home after work, stay with her children, the husband would get home around 6, then she would normally leave the house then come back at a later time."

In 1995, Craig Stebic was charged with two felony counts of unlawful use of a weapon, according to the Tribune.