A 2 1/2-month investigation by sheriff's deputies and state police in Southwest Virginia has failed to produce an explanation for mysterious disturbances at two mountain homes near the West Virginia border last December that topped furniture and books and shattered dishes.

"It's just one of those mysterious things you never find an answer to," Giles County Deputy Sheriff Jimmy Niece said yesterday.

County Sheriff John Hopkins III said the investigaion of the four incidents that occurred in Pearisburg, Va., a factory town located about 250 miles southwest of Washington, "is closed."

Dr. J. G. Pratt of the University of Virginia medical school, who said the Pearisburg incidents are typical of hundreds of documented cases of psychic phenomena, said he was not suprised that the law enforcement officers were unable to find an explanation.

The disturbances began Dec. 19 in the home of Beulah Wilson a 65-year-old widow who lived with her 9-year-old foster son on Fletcher's Mountain.

Mrs. Wilson said objects began falling off a kitchen cabinet, dishes shattered and large pieces of furniture toppled. She said she never saw things fall because they fell behind her, but said the little boy saw everything.

Mrs. Wilson, whom neighbors described as an upstanding and responsible member of the community, moved into her son's home because of the disturbances.

Mrs. Wilson's son. Donald, said that on a visit to his mother's house on Dec. 20, a similar incident happened. The 9-year-old foster son was standing at the foot of the stairwell when a cabinet nearby toppled, Wilson said.

Three nights later, on Dec. 23, Wilson said, something unusual happened at his home - a table and a trophy toppled for no apparent reason.

The next day, Christmas Eve, Wilson said , te foster son went upstairs in his house and things began falling again. He said books began falling out of a hallway bookcase as if someone were throwing them. He said he could see that the boy was not throwing the books and that the disturbance stopped once he took the boy outside.

The Wilsons returned the boy to the County Welfare Department after the Christmas Eve inciden. Sheriff's deputies said the family has experienced no unusual occurrences since the boy left them.

Deputies and county welfare officials said no similar incidents have occurred in the new foster home where the child has been placed.

"He's doing fine," Linda Boggs, a county welfare supervisor.

Pratt, the University of Virginia professor, said he believes the child possesses psychic energy, which, when released, causes objects to move. He said the case follows "the typical pattern of poltergeist phenomena.",

He said normally the cases "begin unexpectedly, run their course, then unexpectedly stop."

The sheriff's department rejects the parapsychologist's theory. "I don't believe in ghosts," said Niece, one of the chief investigators in the case. "I feel it was humanly done, but I can't prove it," he said.

The Pearisburg incidents stirred rumors of supernatural happenings and a host of inquiries from local and national media. Television camera crews trekked up th long, winding road to the Wilson home to film the exterior of the house.

A neighbor said Mrs. Wilson moved back into her house last Friday.

The Wilsons could not be reached for comment.