Using a Corner-type potential for the interaction between two mono-axial molecules and choosing a special form for the dependence on the relative orientations of these molecules, we derive a simple equation for the angular dependence of the single particle distribution function. Given this function we obtain algebraic expressions for the elastic constants for splay, twist and bend, in which the dependence on the four parameters, occurring in the potential, is shown explicitly. We obtain good agreement with the experimental data for the order parameters and the elastic constants.