Painting of Tarpon in the Texas surf. From spring to late fall the tarpon frequent the beach on South Padre Island and the Jetties in Isla Blanca Park. They can be caught from the beach or boat. Larry Haines once battled a Monster Tarpon for five hours that he hooked while fly fishing. That fish story is legendary and true! The tarpon ranges in size from 40 to 200+ pounds and can be sight casted in the clear surf.