To estimate the effects of temperature- and pressure-dependent viscosity on passive flow beneath mid-ocean spreading centers, we have developed a numerical approach combining a finite element method to solve for the three-dimensional flow and a finite difference solution for temperatures. This numerical method is applied to study an idealized spreading center consisting of a 100-km transform fault offsetting two ridge segments. Viscosities are given according to the temperature and pressure dependence of thermally activated creep for Newtonian and non-Newtonian rheology. Melt production rates are calculated by using an adiabatic melt relation and our flow and temperature fields. The density variation of mantle due to thermal expansion is converted into gravity anomaly. The results are compared with those of a model with uniform viscosity. The thickening of the high-viscosity layer causes mantle upwelling in the variable-viscosity model to be stronger but narrower. Faster upwelling reduces heat loss to the surface during ascent, leading to greater melt production. Under the same boundary conditions, the variable-viscosity model creates thicker crust and the predicted thickness is more nearly independent of spreading rate. The zone of melt production is narrower and the rate of melt production decreases more abruptly near the transform fault. The gravity anomaly caused by the mantle thermal structure for the variable-viscosity model is similar to that of the constant-viscosity model with a maximum difference of a few milligal. ¿ American Geophysical Union 1992