The environments of supernova explosions are often inhomogeneous, and there may be jumps in their density structure. We have developed a semianalytic model under the thin-shell approximation for supernova remnants that evolve crossing a density jump in the ambient medium. The generic evolutionary relations are presented for the blast wave after impacting on a cavity wall, which may be produced by the energetic stellar wind from the supernova progenitor. The relations can also be extended to the case in which the blast waves break out from a dense cloud if a different density contrast is used. This model is applied to N132D, a well-known cavity-born supernova remnant whose evolution has not yet been quantitatively estimated in a cavity scenario because of the lack of model formulae, and self-consistent physical parameters are obtained.