Iteration techniques, including successive underrelaxation (SUR), Gauss‐Seidel (G‐S), and successive overrelaxation (SOR) schemes, were adapted to solve finite element equations of aquifer contaminant transport. Numerical experiments were performed to assess the convergency of these iteration schemes. When the mesh Peclet number is much less than one, all three iteration schemes generate convergent computations. When the mesh Peclet number is greater than one, only SUR and G‐S schemes yield convergent calculations, whereas the SOR scheme leads to divergent computations. The relative merits of the successive iteration to direct elimination methods in terms of CPU memory and CPU time requirements are compared through two simple examples. For all practical problems, successive iteration schemes offer substantial savings in the central processing unit (CPU) memory over the direct elimination scheme, without complicating the programming; the larger the problem, the more the saving. For small problems the successive iteration schemes, if convergent, require comparable CPU time to that required by the direct elimination scheme. However, for large problems, the successive iteration schemes consume only a small fraction of the CPU time used by the direct elimination scheme.