We propose streamline-based simulation as a possible alternative to particle tracking for modeling solute transport. Like particle tracking, the pressure field is computed on an underlying grid using conventional techniques. The flow velocity at cell edges is then computed using Darcy's law, and this information is used to trace streamlines throughout the domain. In particle tracking, mass is transported by moving particles along streamlines. In the method we describe, a one-dimensional conservation equation is solved numerically along each streamline. If the flow field changes, the solute concentration is mapped onto the underlying grid and the streamlines are recomputed. The concentration is then mapped back onto the new streamlines, and the simulation proceeds as before. The method is suited for modeling advectively dominated multispecies transport in heterogeneous aquifers. We illustrate the streamline approach with synthetic example problems in fully saturated, confined aquifers: conservative, sorbing, and decaying tracer; a four-component radioactive decay chain; and saltwater intrusion where the flow field changes with time. Where possible, we compare the results with analytical solutions and results from particle tracking codes. ¿ 1999 American Geophysical Union