Results are presented of the calculation of the laminar boundary layer on infinitely long elliptic cylinders in a supersonic perfect gas flow at an arbitrary angle of attack. It was assumed that the Prandtl number is constant and equal to 0.7, the dynamic viscosity coefficient follows a power-law variation (μ ≈ T0.76) with temperature, and there is high heat transfer at the body surface (H1w=0.05). The calculations showed that a change of the body shape—the ellipticity coefficient δ=b/a—has a significant effect on the nature of the distribution and the magnitude of the local heat flux. In evaluating the thermal fluxes at the blunt leading edges, swept wings are usually considered as infinitely long yawed cylinders. In studying heat transfer at the surface of bodies of small aspect ratio at high angles of attack, wide use is made of the hypothesis of plane sections, when each section, orthogonal to the longitudinal axis of the body, is considered equivalent to a corresponding yawed infinite cylinder. By now quite detailed studies have been made of the behavior of the boundary layer on an infinitely long yawed circular cylinder with both the laminar and turbulent flow regimes for a compressible gas [1, 2]. However, there are no data on the heat transfer at the surface of a yawed infinite cylinder with arbitrary cross section, although the availability of such data is urgently needed, for example, for the proper selection of the form of the leading edges of the swept wing. This article presents the results of the calculation of the characteristics of the laminar boundary layer on the surface of infinite elliptic cylinders in a supersonic perfect gas flow. The calculations were made over a quite wide range of flight Mach number M, yaw angle λ, and ellipticity factor δ. The data presented on the distribution of the relative heat flux along the cylinder directrix may be used also for estimating the heat flux with account for the real properties of air if we know the corresponding value of the heat flux in the vicinity of the stagnation line.