The steam reforming of methanol was investigated in a catalytic Pd–Ag membrane reactor at different operating conditions on a commercial Cu/ZnO/Al2O3 catalyst. A comprehensive two-dimensional non-isothermal stationary mathematical model has been developed. The present model takes into account the main chemical reactions, heat and mass transfer phenomena in the membrane reactor with hydrogen permeation across the PdAg membrane in radial direction. Model validation revealed that the predicted results satisfy the experimental data reasonably well under the different operating conditions. Also the impact of different operating parameters including temperature, pressure, sweep ratio and steam ratio on the performance of reactor has been examined in terms of methanol conversion and hydrogen recovery. The modeling results have indicated the high performance of the membrane reactor which is related to continuous removal of hydrogen from retentate side through the membrane to shift the reaction equilibrium towards formation of hydrogen. The obtained results have confirmed that increasing the temperature improves the kinetic properties of the catalyst and increase in the membrane's H2 permeance, which results in higher methanol conversion and hydrogen production. Also it is inferred that the hydrogen recovery is favored at higher temperature, pressure, sweep ratio and steam ratio. The model prediction revealed that at 573 K, 2 bar and sweep ratio of 1, the maximum hydrogen recovery improves from 64% to 100% with increasing the steam ratio from 1 to 4.