Ionic concentrations and electric field space profiles in one dimensional membrane are described using Nernst-Planck-Poisson (NPP) equations. The usual assumptions for the steady state NPP problem requires knowledge of the boundary values of the concentrations and electrical potential difference. In analytical chemistry the potential difference may not be known and its theoretical prediction from the model is desirable. The effective methods of the solution to the NPP equations are presented. The Poisson equation is solved without widely used simplifications such as the constant field or the electroneutrality assumptions. The first method uses a steady state formulation of NPP problem. The original system of ODEs is turned into the system of non-linear algebraic equations with unknowns fluxes of the components and electrical potential difference. The second method uses the time-dependent form of the Nernst-Planck-Poisson equations. Steady-state solution has been obtained by starting from an initial profiles, and letting the numerical system evolve until a stationary solution is reached. The methods have been tested for different electrochemical systems: liquid junction and ion selective electrodes (ISEs). The results for the liquid junction case have been also verified with the approximate solutions leading to a good agreement. Comparison with the experimental results for ISEs has been carried out.