Mechanical forces generated by cells modulate global shape changes required for essential life processes, such as polarization, division and spreading. Although the contribution of the cytoskeleton to cellular force generation is widely recognized, the role of the membrane is considered to be restricted to passively transmitting forces. Therefore, the mechanisms by which the membrane can directly contribute to cell tension are overlooked and poorly understood. To address this, we directly measure the stresses generated during liposome adhesion. We find that liposome spreading generates large traction stresses on compliant substrates. These stresses can be understood as the equilibration of internal, hydrostatic pressures generated by the enhanced membrane tension built up during adhesion. These results underscore the role of membranes in the generation of mechanical stresses on cellular length scales and that the modulation of hydrostatic pressure due to membrane tension and adhesion can be channelled to perform mechanical work on the environment.