Three-dimensional hypersonic flow of chemically nonequilibrium air past a sharp, nonslender, elliptic cone at the angle of attack and the slip angle is considered within the framework of the model of hypersonic thin viscous shock layer (TVSL). The applied method makes it possible to solve three-dimensional problems in the absence of planes of symmetry in the flow, does not call for preliminarily solving the Stefan-Maxwell relations with respect to diffusion fluxes, and does not involve excessively time-consuming computer calculations. Peculiarities of the behavior of the equilibrium wall temperature are considered for various types of reentry trajectories. Basic regularities of chemical reactions proceeding in a shock layer and at the surface of a body are studied for various shapes of the body and various values of the angle of attack and the slip angle.