A computer modelling method for the three-dimensionaldynamic analysis of liquid crystal display cells is presented. Themethod is based on a variational approach to the Oseen-Frank freeenergy formulation considering three elastic constants and uses avectorial representation of the director field. A simpler approximateform that uses only two elastic constants but is faster to operate isobtained as a by-product of the full three-constant modelimplementation. The modelling uses finite elements on a mesh oftetrahedral elements for the calculation of directors and electricpotentials while finite differences in time are used in the time steppingprocess. Comparisons are made with results from a 2D dynamicprogram using a tensor model giving good agreement.