This paper presents results of a theoretical and computational study of the title problem. Theoretical arguments lead to simple relations for the effect of free-stream conicity on shock stand-off distance and stagnation-point heat flux. The computational study considers flow of nitrogen at 4.4 km/s over a sphere and a capsule shape. In the case of the sphere the computational results agree very well with theory. However, the flow over the capsule is much more sensitive to the effect of conicity. The increase in heat flux resulting from the conical free stream contributes to the heat flux augmentation observed in shock tunnel experiments on capsule shapes.