A simple lattice model is developed to describe the adsorption at a planar surface of rigid rods restricted to three mutually orthogonal orientations—two parallel and one normal to the surface. Surface exclusion effects by the adsorbed rods are automatically included in the present lattice model treatment. General expressions for the surface pressure versus coverage and adsorption isotherms are obtained over the entire range of surface coverage. When nearest neighbor attractive interactions prevail between the rods, phase separation results at temperatures below a critical temperature. The coexisting equilibrium phases are characterized by different surface coverages and order parameters. The critical temperature, coverage, and order parameter depend on and are determined for various choices of the length-to-breadth ratio of the rods and the strength of the surface–rod interaction. A brief comparison is made of the surface pressure isotherms obtained from the present model with those observed for monolayers formed by lyotropic molecules.