A tyre for vehicles which does not require pressurisation by means of a pressurised fluid has a tread, two sidewalls, and two beads which are attached to a wheel rim made of elastomer material, and is provided with at least one tubular reinforcement body which is associated with the tread; each of the sidewalls having a respective homogeneous resilient annular membrane, a straight generatrix of which forms an angle (A) other than 90° with the axis of the tyre; the membranes being stretched radially between the tread and the beads such as to be pre-tensioned in the absence of external loads acting on the tyre.