This paper is devoted to the modeling and numerical optimization of proton-exchange membrane (PEM) water electrolysers for operation at elevated pressures (up to 130 bars). The model takes into account different geometrical parameters of the PEM cell, the kinetics of the hydrogen and oxygen evolution reactions, the electro-osmotic drag of water molecules, the permselectivity of the solid polymer electrolyte and associated gas cross-over phenomena. The role of various operating parameters (such as pressure, temperature, current density, flow rate of water) on cell efficiency, faradaic yield and heat produced during water electrolysis is evaluated and discussed. The model is also used for the purpose of optimizing the performances of PEM cells. In particular, optimal values of some critical operating parameters (current density, rate of water supplied to the anodes) are recommended.