Virginia's Republican state chairman, George N. McMath, yesterday resigned his party post, attributing his departure to increased business demands and health problems.

McMath asked the Republican State Central Committee to meet next week to choose his successor.

McMath's resignation came a day after the 46-year-old Eastern Shore newspaper publisher and former legislator confirmed reports that he was considering quitting the post he has held since 1974.

The GOP chairman said he had reached his decision "after weeks of contemplation" and despite the urgings of party leaders that he stay on.

"I am deeply grateful to all the good Virginians who have worked with me during my service, and I am appreciative of all the party leaders who have given their cooperation through the years," McMath said in a statement released from party headquarters in Richmond.

But, he concluded, "considering the unceasing demands of my business and the ever-growing needs of the party, I feel that I must now step down."

The committee will meet June 2 to choose an interim successor to McMath. A permanent chairman will be elected at the party's state convention in Roanoke June 29-30.

The first indications of McMath's imminent resignation came Tuesday when a Richmond newspaper reported he was expected to quit shortly because of emotional and physical stress caused, in part, by his duties as state chairman.

Just two months ago McMath was considering an election race against incumbent state Sen. William E. Fears (D-Accomack). He dropped his campaign plans, however, after deciding it would divert too much attention from his business and party chairmanship duties.

Yesterday, in a letter to the state GOP committee, McMath said he had decided that "in fairness to the business, I must devote more time to it."

McMath, a former Democratic member of the House of Delegates who switched parties in 1972, also cited recurring problems with his throat and an old back injury as contributing to his decision to resign.

"Perhaps my greatest medical problem is that I, frankly, have become very tired," McMath said. "This is difficult for me to admit since I always have considered myself to have an abundance of energy."

McMath's newspaper chain, Atlantic Publications, Inc., has grown from 12 to 17 weeklies in the past year-and-a-half.At the same time, he said, his work as party chairman "consumes an average of 50 hours per week, thus leaving me with much business to undertake in whatever hours are left."

Republican Gov. John N. Dalton was traveling on a trade tour of the Far East and his office had no comment from him on McMath's resignation. Other party leaders, however, were quick to praise his contributions to the state GOP.

McMath's organizational skills are largely credited with contributing to the party's almost unbroken success in recent statewide elections. As GOP chairman, he increased the party budget from $120,000 to about $500,000 and increased its technological and staff resources.

McMath had considered resigning once before, in 1977, but changed his mind and became increasingly involved in the party organization.

Most GOP officials yesterday, expressed surprise at his sudden departure. But they quickly turned their attention to speculation about McMath's possible successor.

Among those mentioned as possible candidates for the party post are William Royal, a key Dalton aide who is leaving at the end of the month; former Del. Wyatt Durrette, of Fairfax; Tom Byrd, the recent Republican convert who is the son of Sen. Harry F. Byrd Jr. (I-Va.); and Rick Gray, the Secretary of the Commonwealth. CAPTION: Picture, GEORGE N. McMATH . . .quit after weeks of contemplation