Supercomputers can expand greatly the possibililies for modelling subsurface solute transpot. The theory relating to a specific application, viz., multicomponent solute transport, is presented. It is demonstrated that multidimensional realwor1d problems involving a series of chemical reactions requires significant computational power. It is demonstrated, however, that obtaining true supercomputer performance depends on algorithm selection. Other supercomputer applications are discussed, including visualization and effects of scale-dependent aquifer heterogeneity.