The D.C. Bar is expected to ask the District Court of Appeals to approve an Interest on Lawyers' Trust Accounts program here soon to help generate money for the disadvantaged who cannot afford legal help.

Twenty-seven states have such programs, to cash in on short-term trust funds for which it often is impractical for attorneys to set up interest-bearing bank accounts.

"I think it's a terrific idea," said bar President Marna Tucker. "If some people are resistant now, it's only because they don't understand how it works. Once they understand the concept, I'm sure they'll approve."

A bar committee recently reported that a trust interest program here could generate as much as $100,000 in interest annually, making upwards of $50,000 available for legal services and other community-spirited activities.

When lawyers are entrusted with funds for only a few days, it often is too expensive to set up an interest-bearing bank account, so the funds are put in noninterest-bearing accounts instead. Under the trust interest program, short-term trusts would be pooled by many firms in one permanent account that generates interest.

A study commissioned by the bar found that nearly 80 firms expressed a strong interest in the program, with a potential pool of $2 million.

The Reagan administration, criticized for its cuts in funds for legal services, has encouraged local bars to establish such programs.