Story highlights The captain of a charter fishing boat witnessed the crash

The aircraft went down in shallow water in an area know as West Bay near Galveston

The World War II-ear plane was used to give rides to people seeking a flying experience

A vintage P-51 Mustang aircraft crashed in the Gulf of Mexico near Galveston, Texas, Wednesday, killing two people on the plane, authorities said.

The World War II-era aircraft, owned by the Lone Star Flight Museum and known in recent years as the "Galveston Gal," was used to give rides to people seeking a flying experience.

According to U.S Coast Guard spokesman Petty Officer Steve Lehmann, the captain of a charter fishing boat called the Coast Guard about 11:40 a.m. (12:40 p.m. ET) Wednesday to report he had just witnessed a plane go down between Chocolate Bay and Galveston Bay. The Coast Guard sent a small boat and a helicopter and also called state and local authorities and a volunteer rescue group.

They found the plane in about 3 to 5 feet of water, with both occupants dead, officials said. Names of the victims were not immediately released.

Sgt. John Sampa of the Texas Department of Public Safety, said the plane crashed in an area known as West Bay.

Federal Aviation Administration records say the plane was built in 1944. According to the museum's web site, the plane was converted to a two-seat, dual-control training aircraft while serving in the El Salvadoran Air Force in the 1960s. In recent years, it was painted with the "Galveston Gal" markings and was used to give people a flight experience for about $2,000 a flight.

In 2011, a highly-modified P-51 Mustang crashed into a group of spectators at the Reno Air Races in Nevada, killing the pilot and 10 others, and injuring more than 60 people.