Squeezing system that comprises at least one female drum (1) and at least one male drum (2), one close to the other and which rotate in a synchronous manner, one in the opposite direction to the other, the female (1) having on its side at least one cavity (6) apt for lodging the fruit to be squeezed, and the male drum (2) likewise having on the side at least one protuberance (5) apt for engaging in a portion of the rotation path and apt for being tightly lodged in the cavity (6) of the female drum (1) during each rotation, compressing and squeezing the fruit; the rotation axle (3) of the female drum (1) not being parallel to the rotation axle (4) of the male drum (2), both crossing at a point in space, being preferably coplanar and concurrent and being deployed one with respect to the other at an angle other than 0° or 180°, in which the female (1) and male (2) drums have one of their bases larger than the other, preferably adopting a a frustoconical shape.