The nation's first privately funded rocket soared into space on a near-perfect mission today as spectators on a cattle ranch on the south coast of Texas yelled, "Long live free enterprise."

After years of planning and one explosive failure a year ago, Space Services Inc. of America successfully launched a 37-foot rocket on a 10-minute, 40-second flight, opening up a potential method of relatively inexpensive space transportation for companies that want to put up their own satellites without the help of the government.

The first commercial mission of a European effort to compete with the space shuttle failed late yesterday when the satellite-carrying rocket Ariane crashed into the sea, 14 minutes after it was launched from French Guyana, Agence France-Presse reported.

Conestoga I, the solid fuel rocket whose motor was purchased from National Aeronautics and Space Administration for $365,000, leaped off its small, concrete launch pad about 11:15 a.m. Washington time and roared into a brilliant blue sky, leaving behind a feathery, white trail and the cheers of hundreds of spectators gathered in a party atmosphere on Matagorda Island, 45 miles northeast of Corpus Christi.

"Everything worked perfectly," said former astronaut Donald K. (Deke) Slayton, who joined SSI after retiring from NASA and headed the launch team on the island.

Conestoga I rose 196 miles from the earth and traveled 326 miles downrange before dropping into the Gulf of Mexico and presumably sinking. Conestoga rockets are not designed to be recovered. Along the way, the booster successfully separated a shroud covering the mock payload from the upper stage of the rocket. The mock payload weighed 1,097 pounds and included 40 gallons of water, which was ejected at peak altitude in part as a visual marker. The angle of the sun, however, prevented the launch team from being able to see it.

"It went just right straight up like it was supposed to," said beaming SSI chairman David Hannah, who has pursued the dream of launching a privately funded rocket since reading an article on space potential in Smithsonian Magazine several years ago.

Hannah, a Houston real estate developer who watched the launch with his wife from a green bench outside the trailers at mission control, said the successful launch -- which he compared in technical difficulty to NASA's Mercury Redstone of 1961 -- was a giant step forward for his two-year-old company.

"To be able to walk into a customer and say you've launched a rocket really makes a difference," he said.

SSI hopes to send up an orbital test flight in two years and begin commercial operations shortly thereafter.

Today's celebration was tempered by the death of Toddie Lee Wynne, Hannah's first outside investor and the owner of the ranch from which the rocket was launched. Wynne, 84, died before dawn this morning. He had planned to attend the launch.

After the launch, delayed for one day by mechanical problems, several SSI officials popped open a bottle of hastily purchased champagne to toast the successful mission, David Hannah and free enterprise.

Holding up his glass, Lee Scherer, former director of the NASA's Kennedy Space Center and now an SSI consultant, said, "You can't do this at a government launch site."

Today's venture had a unique Texas quality about it, with much talk among the Texas investors about the glories of free enterprise and the success of the effort dependent in large part on work already done by the government.

In addition to buying the booster from NASA, SSI was aided by various subcontractors with considerable government experience and a variety of ex-NASA officials advising them.

As an exercise in space technology, today's launch broke no new ground. But in assembling a team, raising the private capital and organizing the launch, Hannah has pushed the American space efforts in a new direction.

SSI hopes to mine a potential market in low-earth satellites for oil and other companies that want cheaper or more specialized service than they can get now. Comparing SSI's strategy with the development of small personal and business computers, Charles Chafer, SSI vice president, said today, "We hope to develop a whole new market."

The company is negotiating for a permanent launch site in Hawaii.

In addition, Scherer is exploring the possibility of leasing the Atlas Centaur launch site in Florida to give SSI the capability of sending up heavier communications satellites to higher orbit.

"The only missing ingredient," he said, is a high-level statement from the Reagan administration that "this is in the national interest."

That would put SSI in competition for business with NASA's space shuttle and the European space effort.

Agence France-Presse added:

The motor of the European space rocket Ariane, carrying a telecommunications satellite and a weather satellite, stopped about 30 seconds too early, according to technicians at the space launching center in Kourou, French Guyana.

"The third-stage motor stopped too soon, and then we lost all trace of the rocket," said Frederic D'Allest, general director of the French National Center of Space Studies, 35 minutes after launch.

Andre van Gaver, a top official in the program, said at the project headquarters in Evry, France, that there was a slight chance the two satellites were in orbit, but that they would be in the wrong place and "therefore unusable."

The Ariane program was developed by the European Space Agency, a 10-nation consortium which spent $1.6 billion on the project. Yesterday's crash was the second failure in five attempts to launch Ariane rockets. The two previous attempts succeeded, although they carried no commercial payloads.