The random-walk method for simulating solute transport in porous media is typically based on the assumption that the velocity and velocity-dependent dispersion tensor vary smoothly in space. However, in cases where sharp interfaces separate materials with contrasting hydraulic properties, these quantities may be discontinuous. Normally, velocities are interpolated to arbitrary particle locations when finite difference or finite element methods are used to solve the flow equation. The use of interpolation schemes that preserve discontinuities in velocity at material contacts can result in a random-walk model that does not locally conserve mass unless a correction is applied at these contacts. Test simulations of random-walk particle tracking with and without special treatment of material contacts demonstrate the problem. Techniques for resolving the problem, including interpolation schemes and a reflection principle, are reviewed and tested. Results from simulations of transport in porous media with discontinuities in the dispersion tensor show which methods satisfy continuity. Simulations of transport in two-dimensional heterogeneous porous media demonstrate the potentially significant effect of using a nonconservative model to compute spatial moments and breakthrough of a solute plume. ¿ American Geophysical Union 1996