The Securities and Exchange Commission has closed an 18-month investigation into Mobil Oil Corp., apparently finding no fault with company president William P. Tavoulareas, whose son became an owner of a shipping firm in 1974 that operates Mobil-owned supertankers.

Neither Mobil nor SEC officials would comment on the closing of the investigation. But Mobil's corporate law firm, Milbank, Tweed, Hadley & McCloy, said in a July 23 letter to Tavoulareas' personal attorney that the case is closed.

"As a result of a number of recent discussions with staff of the SEC enforcement division, we understand that the investigation has been completed and that no further SEC proceedings are contemplated," the letter said.

The SEC notified one congressional subcommittee of the completed investigation. The House Commerce subcommittee on oversight and investigations, chaired by Rep. John D.Dingell (D-Mich), had begun an investigation into the shipping transactions at about the same time the SEC began its inquiry.

Yesterday, the subcommittee's counsel, Michael Barrett, said his staff will resume its investigation and will review proposed SEC staff recommendations for enforcement actions against Mobil that did not reach the commission.

"My understanding is that they [SEC officials] recommended something at the staff level . . . and we want to look at the SEC files to see what it was," Barrett said.

Mobil, the second-largest oil company in the nation, has maintained that everything about Tavoulareas' dealings with his son was proper and fully disclosed in public releases. But the subcommittee chairman and the SEC staff disputed the adequacy of the disclosure. Barrett said that SEC enforcement officials negotiated with Mobil over a proposed consent decree from August 1980 up to this summer without success.

William Tavoulareas and his son, Peter, who was 24 when he became a partner in the London-based shipping firm, Atlas Maritime Co., filed a lawsuit against The Washington Post in November, 1980, claiming that the original Post story detailing the shipping transaction was "false and defamatory."

The Tavoulareases have also filed lawsuits against George D. Comnas, a former Exxon executive who was once the senior partner of Atlas, and Philip Piro, Tavoulareas's former son-in-law. Those suits allege that Comnas and Piro provided alleged false information to The Post and the House subcommittee.