Theoretical studies of a planar version of the Lebwohl-Lasher model are presented. The model consists of a set of interacting centres forming a simple square lattice. The pair potential is nearest neighbour and varies as the second Legendre polynomial of the relative orientation between the two particles. The system is studied with the aid of Faber’s theory of nematic order, the mean field theory and the two site cluster theory. The results are compared with one of the existing simulations. We find that Faber’s theory not only gives an accurate description of the model at low temperatures, but also correctly predicts the dependence of various parameters on the system size. The two site cluster theory predicts the order-disorder transition temperature with greater accuracy than the mean field theory.