This paper develops equations for the transmembrane potentials (Vm) that occur in two-dimensional (2-D) sheets of tissue in response to field stimulation from an electrode near but not on the surface of the tissue. Comparison of results with those for one dimension shows that an additional term is present in the 2-D equations that influences the evolution of Vm in the interval between the end of the stimulus and the active propagation that may follow. The results provide an analytical framework for understanding Vm in response to field stimulation in two dimensions, both during the tissue's critical linear phase and thereafter.