A new three-dimensional model of solute transport in groundwater that is based on a widely used two-dimensional method of characteristics model and is coupled to a modular finite-difference flow model is under development. The model's accuracy for ideal aquifers having homogeneous properties, uniform boundary conditions, and steady flow along a grid direction is demonstrated by comparison with conventional analytical solutions. The effect of spatially and temporally variable flow velocities is investigated by comparison with special analytical solutions. To test the performance of the model for typical hydrogeologic conditions, we compare results with those from other models as well as with results from the same model using smaller grid spacings and time steps. This model generally provides accurate results for realistic simulations, and is particularly efficient for advection-dominated transport.