A new method for performing molecular dynamics simulations under constant pressure is presented. In the method, which is based on the extended system formalism introduced by Andersen, the deterministic equations of motion for the piston degree of freedom are replaced by a Langevin equation; a suitable choice of collision frequency then eliminates the unphysical "ringing" of the volume associated with the piston mass. In this way it is similar to the "weak coupling algorithm" developed by Berendsen and co-workers to perform molecular dynamics simulation without piston mass effects. It is shown, however, that the weak coupling algorithm induces artifacts into the simulation which can be quite severe for inhomogeneous systems such as aqueous biopolymers or liquid/liquid interfaces.