The Justice Department has reopened its criminal investigation into charges by Adm. Hyman G. Rickover and others that Newport News Shipbuilding and Dry Dock Co. submitted exaggerated and fradulent claims on nuclear-powered ships it built for the Navy at its huge Virginia yard.

Twenty officials of the shipyard have been subpoenaed to testify next week before a federal grand jury in Alexandria, according to martitime sources familiar with the case.

It is the third grand jury to investigate the allegations, said to involve millions of dollars in shipbuilding contracts. The first, empaneled in Richmond in October 1978, concluded its deliberations in April 1980 without returning an indictment. An individual familiar with that investigation said there were more than 200 people either summoned before that jury or interviewed by the FBI. Still more witnesses were called in the second investigation, also in Richmond, which lasted about three months and also failed to produce any charges.

The Newport News Daily Press yesterday reported that the investigation was reopened at the urging of Rickover, who, the paper said, has pressed the U.S. attorney's office to review the situation ever since the first grand jury failed to return indictments. Rickover refused yesterday to speak with a reporter and a Navy spokesman referred all calls to federal prosecutors.

U.S. Attorney Justin Williams could not be reached for comment and an assistant declined to comment on the case. A shipyard spokesman refused to speculate on why the latest investigation was called.

An individual familiar with the case said, however, that Williams reportedly said he was not satisfied with the prior investigations. Eighteen of the 20 company officials subpoenaed to testify next week had testified in the prior investigations, the individual noted.

The first grand jury was empaneled to determine whether fraud was involved in the shipyard's $943 million cost overrun claims on several nuclear-powered ships. The builders have consistently maintained that the additional claims are for Navy-ordered changes or for late or defective government equipment for the ships.

The shipyard and the Navy settled the dispute for $209 million, just 13 days before the first grand jury issued subpoenas. The settlement did not involve allegations reportedly made by Rickover that the yard had inflated costs, although a maritime source said the company may have settled in order to avoid more litigation over the claims.

The latest investigations reportedly involves the same claims, which the shipyard submitted between 1973 and 1976. Since the statute of limitations is five years, the new grand jury may have to act by March.