The reflection of plane elastic waves from a free surface of monoclinic incompressible materials is examined under plane strain conditions in a plane of material symmetry. The propagation condition is derived which together with the law of reflection yields an inequality that defines the range of existence of the two (one homogeneous and the other homogeneous or inhomogeneous) reflected waves in terms of the angle of incidence of a homogeneous wave, the orientation of the free-surface with respect to a material axis of symmetry, and the elastic constants of the monoclinic material. The critical orientation beyond which there exist two homogeneous reflected waves is derived in explicit form in terms of the elastic constants. One of these reflected waves has an angle of reflection equal to the angle of incidence only for specific orientations which are found. In the range of existence of the two reflected waves, exclusion points are defined for which there exists only one reflected (homogeneous) wave with nonzero amplitude.