The kinetic theory of axially elastic spherocylinder molecules is used for obtaining the shock structure in a vibrationally relaxing diatomic gas. A trimodal and a quadrimodal ansatz are proposed for the distribution function within a shock, and a moment method is used to determine the unknown weight functions in the ansatz. The collision integrals in the moment equations are 22−fold out of which 16−fold integrations are carried out analytically and the remaining integrations are performed numerically using a Monte Carlo technique. The differential equations in the weight functions are solved numerically and shock profiles in nitrogen are obtained for a range of upstream Mach numbers and pressures.