An apparatus for thermoforming plastic containers comprising a pickup station (24), a feeder (25) for feeding flat sheets (8) of thermoformable plastic material to the pickup station (24), at least one thermoforming device (3), and a transferring device (26) for transferring the flat sheets (8) from the pickup station (24) to the thermoforming device (3), the feeder (25) comprising at least one support (50) for a reel (51) of a web (52) of thermoformable plastic material, unwinding means (53) for unwinding the reel (51) of web (52) which are designed, in use, to feed the web (52) along a sliding path extending from the at least one support (50) to the pickup station (24), and a cutting device (54) for cutting the web (52), positioned along the sliding path, for dividing the web (52) into a plurality of pieces each of which corresponds to a flat sheet (8) to be fed to the pickup station (24).