The mixed convection laminar boundary-layer flow in the vicinity of the median plane of symmetry of a finite span wedge is considered where one of the wedge surfaces is kept horizontal. The resulting equations thereof depend on the Prandtl number Pr, the buoyancy parameter K and the Falkner-Skan parameter beta. The self-similar solutions are found to be non-unique for both aiding and opposing flow regimes where in general two dual solutions are obtained; in certain situations eight solutions prevail. The free convection limit is also treated upon considering the asymptotic equations as K --> oo. Numerical results are presented and discussed for both flows for the prescribed wall temperature and wall heat flux conditions.