A numerical method was developed for predicting the pressure-time variation of a sonic boom wave acting on an arbitrary building. The conservation laws for fluid flow were greatly simplified with weak wave approximations and then the numerical technique developed by the Russian mathematician, V.V. Rusanov, was extended to three dimensions and applied. A treatment for two-dimensional as well as three-dimensional building corners was developed. For the first time, Rusanov's technique extended to three dimensions was applied to a sonic boom wave/structure interaction problem. A computer program was written for a sample problem , involving a plane wave oblique to all building surfaces. There were 9,261 mesh points in the field (a 21-sided cube), and the computation was performed on an IBM 360/65 digital computer. The results seem to be physically correct.