A tyre (3) for vehicles which does not require pressurisation by means of a pressurised fluid has a tread (16), two sidewalls (15), and two beads (8) which are attached to a wheel rim (2) made of elastomer material, and is provided with at least one tubular reinforcement body (18) which is associated with the tread; each of the sidewalls having a respective homogeneous resilient annular membrane (24), a straight generatrix of which forms an angle (A) other than 90° with the axis (13) of the tyre (3); the membranes (24) being stretched radially between the tread (16) and the heads (8) such as to be pre-tensioned in the absence of external loads acting on the tyre (3).