VENICE, La. (Bloomberg)—BP P.L.C. and Transocean Ltd. face at least 36 lawsuits, including group cases with potentially thousands of plaintiffs, over environmental damage and personal injuries caused by the oil spill in the Gulf of Mexico.

At least 31 proposed class action suits have been filed in courthouses from Texas to Florida. Commercial fishermen, shrimpers, charter-boat operators and beachfront-property owners asked to represent anyone whose livelihood depends on coastal waters imperiled by the drifting oil. At least 24 cases were filed April 30.

BP has the primary liability for damage caused by the spill, said Keith Hall, an attorney in New Orleans, who isn’t involved in the litigation. He cited a U.S. law passed after the Exxon Valdez oil spill at Alaska in 1989.

“Under the Oil Pollution Act, the fact that it was BP’s oil is enough,” said Mr. Hall, of Stone Pigman Walther Wittmann L.L.C. Plaintiffs “don’t have to show they were negligent or grossly negligent,” he said.

Spokesmen for Transocean and BP didn’t respond to requests for comment on the rapid increase in lawsuits.

Lawsuits also name Cameron International Corp., which provided blowout-prevention equipment, and Halliburton Energy Services Inc., which was involved in cementing the well.

A spokesman for Houston-based Cameron, the second-largest U.S. maker of oilfield equipment behind National Oilwell Varco Inc., said the company doesn’t comment on litigation.

A spokeswoman for Houston-based Halliburton, the second-largest oilfield contractor behind Schlumberger Ltd., said the company is cooperating with investigations into the accident. She said “it is premature and irresponsible to speculate on any specific causal issues.”

The suits are multiplying as the companies struggle to cap a damaged undersea well leaking 5,000 barrels of crude oil a day since the Deepwater Horizon drilling rig exploded April 20. The edge of the spill has begun washing ashore in Louisiana and may reach Florida’s coast early next week.

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