A computer modelling method for the three-dimensional dynamic analysis of liquid crystal display cells is presented. The method is based on a variational approach to the Oseen-Frank free energy formulation considering three elastic constants and uses a vectorial representation of the director field. A simpler approximate form that uses only two elastic constants but is faster to operate is obtained as a by-product of the full three-constant model implementation. The modelling uses finite elements on a mesh of tetrahedral elements for the calculation of directors and electric potentials while finite differences in time are used in the time stepping process. Comparisons are made with results from a 2D dynamic program using a tensor model giving good agreement.