"We are looking at months and months of rebuilding,” she said in an interview. “We want to make sure we have resources to fund all of those phases.”

The fund, which was created only in the past few days, has not identified grantees yet. But Ms. Mountain said the money raised would be used to help families in four main areas: health and housing, schools and child care, work force and transportation, and capital for rebuilding small businesses.

Ms. Mountain, who had family rescued in Houston this week, said none of the money raised for the Rebuild Texas Fund would be used for administrative costs. Instead, the OneStar Foundation and the Dell Foundation would cover those expenses, meaning that “for donors, their contributions are going directly to victims,” she said.

Mr. Dell is a billionaire many times over, having founded Dell, turned it into the largest computer maker in the world, then taken the company private in 2013. He is still chief executive of Dell, and in 2015 orchestrated one of the biggest technology deals ever, the $67 billion purchase of EMC.

Founded in 1999, the Dell Foundation has given away more than $1.3 billion. The $36 million pledge to the Rebuild Texas Fund will not be Mr. Dell’s largest; he gave $50 million to the University of Texas at Austin in 2013.

But Ms. Mountain hopes others will contribute alongside the Dells. Anyone can contribute to the fund by texting “RebuildTx” to 91999 and following the prompts.

“We’re heartbroken,” Ms. Dell said in a statement. “Michael and I are both from Texas, and the street he grew up on is underwater now. We want everyone to know that we are in this for the long haul to support families and communities — our neighbors in need.”