The frame comprises a base (32), two telescopic siderails (33) and mounting means (35, 46) for pivotally mounting each longitudinal member (33) to said base. This frame can be placed in a stowed position, in which said siderails (33) are, on said base (32), in a retracted and transversal position, and into a position of use, in which the siderails (33) are in an extended and longitudinal position. The frame also comprises means for holding the siderails (33) in an extended and longitudinal position opposite said base. The bed comprises the frame and a number of slats (36). The method comprises the step of providing a bed of this type and a step for putting the base (32) in place on first elements fixed to the vehicle as well as steps for moving the bed from a stowed position and into a position of use.