The spatially discretized two‐dimensional solute transport equation in a steady groundwater flow was solved by an eigenvalue technique. The solution is exact in time. An explicit expression was obtained for each nodal point as a function of time. Thus the computer code can be implemented to calculate solute concentration at any nodal point at any given instant with a direct computation. The general solution can be obtained explicitly for transient boundary conditions and variable constant source loads. The solution for steady boundary conditions can readily be derived from the general solution. The method presented herein can provide convenience of data retrieval, particularly in groundwater management modeling.