The brutal beating death last month of Hye Ja Yi, an 18-year-old Korean-born Gaithersburg High School student, left her community aghast and the police stumped.

Her battered body was discovered April 30 at a construction site at Muddy Branch and Fields roads about two miles from the Yi family's Gaithersburg home. The teen-ager had been sexually assaulted "and literally stomped to death," Montgomery County Police said.

Investigators went into high gear last week with an appeal to the public for help, and they have secured commitments for $12,000 in reward money for tips leading to the arrest and indictment of a suspect.

The linchpin for the public appeals is the county's Crime Solvers program, a privately funded, nonprofit organization similar to several in the Washington area that funnel reward money through police to tipsters.

In the case of the Yi slaying, county police publicized it as the "crime of the week" in television and newspaper announcements and offered a $1,000 reward.

This was followed by additional offers of $10,000 from the victim's family members and friends, as well as $1,000 from the Gaithersburg and Upper Montgomery Chamber of Commerce.

Police, who were looking this week for two men for questioning in the case, say that the Crime Solvers action has generated some tips. One of the men had harassed the Yi family earlier; the second had been seen running in the area the morning the body was found. Police said the tip about the runner came to Crime Solvers.

The program has been operating in Montgomery County since November 1978 and to date has paid $60,725 in cash rewards, part of more than $250,000 that Crime Solvers groups throughout the Washington area have distributed since they were created in the late 1970s and early 1980s.

Statistics from police in the District and Alexandria, and in Fairfax, Montgomery and Prince George's counties, show that tipsters have helped solve 2,346 criminal cases and led to the arrests of more than 1,000 suspects since the programs began.

Crime Solvers programs, of which there are dozens in the mid-Atlantic region and more than 400 in the United States and Canada, are each operated autonomously by volunteer boards of business owners and community activists. The boards raise reward money for the police departments from private contributors in their jurisdictions. The police then publicize major unsolved cases, offering up to $1,000 in cash rewards and anonymity to all tipsters.

Callers are not required to give their names. Each is given a number to use in future contacts with police. If a tip leads to an arrest and indictment, the tipster usually is given the reward at a meeting with a member of the Crime Solvers civilian board.

The meetings are arranged at locations such as a doorway to a busy suburban store, for example. The tipster knows the board member's name, but the board member knows the tipster only by the caller number.

"Anonymity, that's the key to the program," said Officer George Ludington, coordinator of the Montgomery County program.

"It's been working pretty good," said D.C. police spokesman Sgt. Joe Gentile.

"It's cost-effective," agreed fellow D.C. Officer Rufino Fisher.

In Prince George's County, where the program has been operating since November 1979, tips through Crime Solvers have helped solve 16 murders, 76 rapes, 71 burglaries, 54 narcotics cases and 11 child abuse cases, said Officer Carol Landrum, coordinator of the county program.

Who calls in tips to police?

"Most of them are people who have heard these jerks running at the mouth, bragging somewhere," Landrum said.

Also, said Officer John Kochensparger, coordinator for the Alexandria police department's program, the tipsters often are the "fringe element between the criminals and law-abiding society . . . . Theirs is the best information."

He added, "I've had calls where the actual suspect was in another room" not far from the tipster, and the caller would have to "mumble and talk low."

Kochensparger said that the percentage of men and women among tipsters "is split down the middle." Women, he said, often "will call on a boyfriend or a husband" after the relationship has been broken up.

"They call out of the circumstances of their lives . . . whereas the men usually call about something they've heard," Kochensparger said.

Arlington County is the only major jurisdiction in the Washington area without a formal Crime Solvers program.

County police spokesman Tom Bell explained: "Originally, the chief was uncomfortable with the idea of paying for information."

But Bell said that later, as the programs became popular in other jurisdictions, Arlington police began publicizing major unsolved cases on a "spot basis."

Bell said that the department has paid a number of small rewards, usually $50 or $100 for minor drug cases, all from department funds, rather than from private sources as with the Crime Solvers programs. The Crime Solvers telephone number for Prince George's County is 735-1111. The number in Montgomery County is 840-2444.