Under pressure from Sen. John C. Stennis (D-Miss.), a Senate investigative hearing on a controversial waterway project in Mississippi has been canceled.

The June 14 hearing by the water resources subcommittee had been scheduled to go into questions about the Tennessee-Tombigbee Waterway, the costliest federal navigation project in history.

But Sen. Mike Gravel (D-Alaska), subcommittee chairman, said he canceled the hearing after Stennis - a leading supporter of the $1.8 billion canal - persuaded him it was not necessary.

Gravel said Stennis had talked to him twice in recent months in an effort to dissuade the subcommittee from taking a look at issues that have made the Army Corps of Engineers barge canal so controversial.

"Sen. Stennis apprised me of the litigation that was pending and I decided a hearing was not necessary. He indicated to me that a hearing would be injurious from a legal point of view," Gravel said.

Environmentalists and the Lousiville & Nashville Railroad are litigating a suit in the federal courts, alleging the corps is illegally building the 260-mile-long waterway almost twice as wide as authorized by Congress.

Stennis raised the same point - that litigation was pending - when he convinced the General Accounting Office in 1977 to withhold a report that suggested the corps had misrepresented costs and benefits of the waterway.

The Mississippi senator did not respond to requests for comment on his role in preventing a Sentate airing of questions about cost overruns, cost-benefit calculations and other matters on the project.

Gravel denied that Stennis had threatened or suggested that the Appropriations Committee, of which he is a senior member, would stop the funding of any of Gravel's pet projects in Alaska.

The possibility of an injury into the Tenn-Tom, as it is known, was stimulated by the introduction of a bill by Sen. Gaylord Nelson (D-Wis.), calling for a halt to the project on the ground that it is "the biggest pork-barrel boondoggle of them all."

Nelson also tried without success in March to convince Secretary of the Army Clifford L. Alexander to stop the corps from awarding a contract on a major segment of the canal.

The contract is for excavation of a 40-mile cut through a ridge of northeast Mississippi to link the north-flowing Tennessee River and the south-flowing Tombigbee.

When completed, the canal in Mississippi, Alabama and Tennessee will shorten the route between the Gulf of Mexico and inland barge shipping points, which now use the Mississippi River, farther to the west.

Authorized by Congress in 1946 and given construction money in 1971, the project has been a favorite of southern legislators in key committee positions who see it as a boon for their region.

Nelson declined comment on Gravel's decision to cancel the Tenn-Tom inquiry next month, although he and Gravel are said to have talked privately-and heatedly-before the decision.

"I've vague about it. I may have said 'yes' to the subcommittee staff about scheduling the hearing," Gravel said. "But when I focused on it and read the stuff in Nelson's speech [on his bill] I decided the hearing was not necessary."

There was nothing vague about Gravel's formal announcement last month saying the June 14 hearing would examine the Tenn-Tom "as it has developed since authorization. Special attention will be given to corps assumption of discretionary authority provided by the authorization."

"Both project supporters and opponents will be on the witness list to address those issues," the Gravel statement said.

Told of Gravel's change of heart, Jon T. (Rick) Brown of Washington, one of the attorneys in the federal court case, said, "The news release had gone out. Commitments had been made. People wanted to testify . . . This is a betrayal of sorts."

Gravel said, "The Tennessee-Tombigbee is a good project. I think it will add to our maritime capacity. I don't need Sen. Stennis to outline the benefits for me."

He added that he was "not disturbed" by questions about the project's economics. And in any case, he said, he did not think a subcommittee hearing would make much difference.

"I went through that for six years with Lock and Dam 26 [a disputed Mississippi River project] and it all amounted to nothing," Gravel said.

"I don't want to rag around with these environmentalists. I've got my own macroview of things and I've got more to say grace over than this-Alaska D-2 lands, federal water policy. Maybe once that's done, we'll grapple with this." CAPTION: Picture, Sen. Stennis, leading supporter of Tenn-Tom canal. By James K. W. Atherton - The Washington Post