Beneath the Planet of the Apes was the first sequel to the 1968 movie Planet of the Apes.
It stars Charlton Heston (although he is in a very small supporting role) and James Franciscus (Burt Reynolds was originally intended for this role). The military Ape General was originally supposed to be played by Orson Welles. The film is not set in 3955, it's set in 3979.
The film picks up where the previous one left off, with another astronaut, Brent (Franciscus), landing on Earth in the year 3955, A.D. (this is a time error, as the first film was set in 3978). Brent discovers Nova, and both figure out Taylor is missing. While trying to find their friend, they discover the City of Apes, who plan to discover secrets hidden in the so-called Forbidden Zone.
Cornelius (played here by David Watson) and Zira (Kim Hunter), tired of the coming revolt, decide to escape Ape City and their world.
In the meantime, Brent and Nova's quest leads them to an underground section of the planet, the "Forbidden Zone" that contains the ruins of what was once New York City. There, Nova is kidnapped and Brent held hostage by a group of white robed mutants, a race called the House of Mendez, decendents of the survivors of a nuclear war from the later 20th century. The mutants use mind control to manipulate Brent.
During the Mendez's religious services, the mutants worship a nuclear bomb, which they claim is their protector (but is, in reality, designed to destroy the entire fake Earth). Brent is brainwashed into participating in the worship services. Afterward, Brent is taken to the prison cells, and there he discovers Taylor. Using the Mendez's mind control, both Taylor and Brent end up in a brutal confronation, but the appearance of Nova breaks up the fighting, enabling both men to turn against their captors.
Taylor, Brent, and Nova attempt to escape the Forbidden Zone when Nova is shot dead by one of the Mendez' mutants. Then, the two astronaut survivors end up confronting the army of apes who have themselves entered the Forbidden Zone.
During the final gunfight, the apes kill Brent, and later shoot Taylor. Knowing he is dying, he decides the only way to stop the violence is by detonating the bomb, which he does, destroying the fake Earth itself. The film ends with a monologue stating that the fake Earth is now dead, and the credits roll in silence against a black screen.
Despite the destruction of the fake Earth, the Planet of the Apes series spawned three more movies. The next film, Escape from the Planet of the Apes, explains that Cornelius, Zira, and a third ape escaped the fake Earth before its destruction by repairing Taylor's ship from the first film and piloting it through a rift in time that takes them back to 20th century Earth (do they went to 20th century Earth in order to stop launching in the future?).
Since Roddy McDowell was unavailable to return for this sequel, David Watson assumed the role of Cornelius.
Charlton Heston showed little interest in reprising his role from the first movie and agreed to appear for only a short stint of filming under the condition that his entire salary would be donated to charity. The producers hired a Soap Opera Actor to fill Heston's shoes, and wisely chose to have Heston's cameo broken into bookended opening and closing sequences in the film.