The validity of approximate equations describing the membrane potential under extracellular electrical stimulation (Meffin et al 2012 J. Neural Eng. 9 065005) is investigated through finite element analysis in this paper. To this end, the finite element method is used to simulate a cylindrical neurite under extracellular stimulation. Laplace's equations with appropriate boundary conditions are solved numerically in three dimensions and the results are compared to the approximate analytic solutions. Simulation results are in agreement with the approximate analytic expressions for longitudinal and transverse modes of stimulation. The range of validity of the equations describing the membrane potential for different values of stimulation and neurite parameters are presented as well. The results indicate that the analytic approach can be used to model extracellular electrical stimulation for realistic physiological parameters with a high level of accuracy.