A semianalytical solution technique is presented for solving Laplace's equation to obtain primary and secondary potential and current density distributions in electrochemical cells. The potential distribution inside a rectangle with the electrodes facing each other between two insulators is presented to illustrate the method. It is shown that the method yields analytic equations for the potential and the potential gradient along the lines. The unique attribute of the technique developed is that the solution once obtained is valid for nonlinear boundary conditions also. The procedure is applied to some realistic problems encountered in electrochemical engineering to illustrate the utility of the technique developed.