A theory is presented capable of describing the structure of a strong shock in a diatomic gas. Strong shocks in a monatomic gas can be effectively treated using the bimodal distribution function of Mott‐Smith. Relaxation effects are included in the present analysis by replacing the bimodal form with a weighted trimodal distribution function. The three weighting functions are determined to satisfy certain averages of the Boltzmann equation. Logical limitations occur when the trimodal distribution reduces to either a monatomic or a diatomic bimodal distribution. The molecular model under discussion is the rigid convex body of revolution. Specific cases include the loaded sphere and the spherocylinder. Solutions are obtained for slightly loaded spheres by applying a method of matched asymptotic expansions. A computer study is performed at infinite Mach number for a spherocylinder corresponding to a hypothetical ``real'' gas. Comparison with recent shock data suggests the possibility of solidly relating the geometry of a spherocylinder to a nitrogen molecule.