The uniform upstream flow constraint of Chapter 4 is removed. Of course, if the shock is two-dimensional (axisymmetric), the nonuniform upstream flow must also be two-dimensional (axisymmetric). This constraint does not alter the jump conditions but substantially alters the tangential and normal derivatives. Earlier assumptions are retained, such as a steady flow of a perfect gas. The flow plane approach means the jump conditions hold in a three-dimensional flow, as before. The normal derivatives still require a two-dimensional or axisymmetric flow. The homenergetic aspect is retained (except in Section 8.6), but the nonuniform upstream flow may be rotational or irrotational. In Section 8.7, an illustrative model is provided where the nonuniform upstream flow is irrotational.