The House Public Works Committee yesterday approved a $3.5 million grant for construction of a massive seawall to stem they rapid erosion that is eating away the shores of tiny Tangier Island in the Chesapeake Bay.

The proposed expenditure, approved as part of an omnibus public works bill, is expected to go to the full House for approval early in the fall.

Rep. Paul Trible (R-Va.) had requested the grant, which would pay for the construction of an 8,200-foot seawall along the island's shoreline.

The three-square-mile island off Virginia's Eastern Shore, is home to about 900 people, most of them descendants of the original families who settled on Tangier in 1686. They long had been used to some erosion, but have grown increasingly apprehensive as large stretches of shoreline were lost to the sea in the last two years.

In 1978, 31 feet of the western shoreline washed away, three times te previous annual rate, according to the records of island resident Asbury Pruitt.

By mid-April this year when another 17 feet of shore had been lost to the waters of the Cheapeake Bay, the residents of the island wre genuinely alarmed.

The study, issued last Dec. 27 by Virginia state officials, showed that "within the coming decade the [island's] airport runway would be inoperable and within two decades part of the inhabited west ridge would have been consumed."

The study attributed the erosion to the great expanse of open water on three sides of the island and to the northwest and southwest winds, as well as to a shortage of sand on the beaches of the tiny island.