A secret attempt by Virginia Lt. Gov. Charles S. Robb to bring union and management together to end the two-day-old strike against the mammoth Newwport News Shipbuilding and Dry Dock Co. failed tonight.

Union members predicted as a result that the strike will be lengthy. "It means that the parties have dug in," said Bruce Thrasher, district director of the United Steelworkers of America. "I don't see any other avenues to explore."

Robb had acted as a conficential intermediary since Tuesday, according to Thrasher, when Robb flew to Washington to meet privately with steelworkers International President Lloyd McBride. Robb also was in contact with shipyard President Edward J. Campbell, although the closest union and management came to negotiating with each other was a telephone conversation between lawyers for the two sides, Thrasher said.

Neither Robb nor company officials could be reached for comment tonight.

The possible agreement that both saides had been exploring, according to Thrasher,included an end to the strike by the steelworkers. In return, the company would have allowed a number of disagreements with the union be subjected to a greivance procedure. The shipyard also would have prepared a written promise to bargain with the union if the company loses a case in the Fourth U.S. Circuit Court of Appeals in which it is callenging the representation election that made the union bargaining agent for the company's 15,500 production and maintenance workers a year ago. The compnay has already said it will not appeal the court's decision if it loses.

Tensions in the strike increased today when six union pickets were arrested. They included Wayne Crosby, 35, president of the shipyard's Local 8888. He and three other union members were charged with interfering with the rights of workers to go to work, a misdemeanor under Viginia's right-to-work law. A seventh person arrested was identified as the husband of a union picket and was charged with assulting an officer and blocking access to a shipyard gate.

Company officials claimed today that between 45 and 20 percent of the yard's 12,000 production and maintenance workers assigned to the day shift crossed picket lines and reported for work. Union officials put the figure at 20 percent.

Many of those manning picket lines around the shipyard, Virginia's largest private employer, seemed convinced the strike will be a long one.

"We're out," said machinist Ryan Gary. "If it takes two years, we've got to beat it... because if we fo back now they'll fire us all."

Shipyard and union officials exchanged charges today, with the company filing papers with the appeals court in Richmond seeking to speed hearings in its appeal of the union's victory in the disputed representation election. Similar petitions were filed by Virginia Gov. John N. Dalton and Attorney General J. Marshall Coleman, citing the economic harm a prolonged strike would do to the state.

Shipyard president Campbell said: "in view of the irresponsible strike currently in progress and the economic hardship it is causing for our employes, our company and the entire Commonwealth, we believe it is necessary to again ask the court to further expedite our appeal."

The union, meanwhile, delivered a stinging criticism of Dalton and the state police after the arrests this morning of local union president Crosby and pickets for allegedly interfering with traffic.

Calling the use of force and dogs by state police troopers during the arrests "extremely provocative," union spokesman Bill Edwards said: "These officers were following orders that we think were delivered, and we assume these ordera came directly from the governor's office."

In Richmond, a spolesman for Dalton called the charges false and said the governor ahd nothing to do with the arrests.

Dalton said last month he would send in troopers to protect employes who chose to continue working under the Virginia right-to-work law. About 90 state troopers are on full-time duty here, along with a helicopter and an armored truck.

Crosby and the others are free on bail pending a hearing Friday in District Court. A city magistrate has ordered Crosby to refrain from picketing, and the Steelworkers charged that the magistrate's order is unconstitutional.