In this study, we investigate film cooling on an inclined flat plate in a laminar supersonic flow. The influence of the most relevant parameters, the Mach and Reynolds numbers of the freestream, the blowing ratio, and the blowing geometry, is examined using numerical simulations and in experiments. Importantly, a correlation factor that describes the effect of the most important parameters for a large range of flow conditions has been developed from a simple heat balance model. Unlike the results for turbulent conditions that are typical for cooling turbine blades, interestingly, we have found that considerably less cooling gas mass flows are needed to cool the surface over a large area. In laminar boundary layers no turbulence appears, so that neither the cooling gas strongly mixes with the main stream nor does the blowing momentum influence the cooling effectiveness, provided that a boundary-layer transition is not induced by the cooling gas injection. Our results, presented here, agree with the results of previous investigations of laminar supersonic flow conditions. Nomenclature C = Chapman-Rubesin factor c p = specific thermal capacity F = blowing ratio FU = flux vector in the x direction GU = flux vector in the y direction HU = vector of the viscosity terms h = enthalpy k = thermal conductivity M = momentum ratio Ma = Mach number _ m c = cooling gas mass flow _ m 0 e = mass flow entering the mixing layer from the main flow Pr = Prandtl number _ q = wall heat flux Re e = unit Reynolds number behind the front shock Re x 0 = Reynolds number based on x 0 s = slot width in the streamwise direction T = mean temperature in the mixing layer T aw;c = adiabatic wall temperature for the case with cooling T r = recovery temperature T 0;c = total temperature of the cooling gas t = slot width in the spanwise direction U = state vector u = velocity in the x direction v = velocity in the y direction x = distance from the leading edge, parallel to the model surface x ref = empirical reference length x s = distance from the leading edge to the center of the blowing opening x 0 = distance from the center of the blowing opening y = distance normal to the model surface = boundary-layer thickness = cooling effectiveness = heat transfer coefficient = dynamic viscosity = correlation factor = density = Mach angle = blowing angle Subscripts c = with cooling nc = no cooling e = boundary-layer edge 1 = freestream 0 = stagnation conditions Superscript * = values determined at the reference temperature