The deformation behaviour of amorphous polymer-rubber blends is investigated in terms of an axisymmetric unit cell model containing an initially spherical rubber particle. The behaviour of the rubber is described by an incompressible non-Gaussian network theory, while for the matrix we adopt a recent large strain elastic-viscoplasticity model that incorporates the intrinsic softening upon yield and the subsequent progressive orientation hardening typical for amorphous glassy polymers. Guided by simple analytical estimates, cavitation of the rubber particle is interpreted in terms of the unstable growth of a pre-existing small void. It is shown that cavitation and yield are essentially coupled processes. On the macroscopic scale, both are softening mechanisms: If macroscopic yield takes place before the limit stress for cavitation is reached, cavitation is prohibited. Furthermore, and contrary to common belief, it is found from the interfacial stress history that, using realistic material parameters, the rubber particle continues to significantly affect plasticity in the matrix in the post-cavitation regime, i.e. after it has cavitated, so that cavitated particles cannot always be considered to be equivalent to particle-sized voids.