Abstract The mechanical behaviour of voided polycarbonate has been predicted by using a detailed finite element model of the microstructure and an accurate elasto–viscoplastic model for the glassy polymeric matrix material. On the microstructural level a spatially periodic plane strain matrix with irregularly distributed voids has been considered. The voids represent low-modulus non-adhering rubbery particles under negative pressure. The constitutive model for the homogeneous parts of the material reflects the typical yield and post-yield behaviour of glassy polymers: strain rate and history dependent yield, intrinsic strain softening and subsequent strain hardening. The finite element simulations show that the irregular void distribution causes a radical change in deformation behaviour. In particular the macroscopic strain softening disappears. This transformation in macroscopic behaviour originates from the arbitrary order in which local shear bands between the randomly distributed voids are formed and subsequently harden. In the averaged overall mechanical response the individual unstable yield and post-yield behaviour of the local shear bands is evened out, resulting in an overall stable macroscopic deformation behaviour. This mechanism is believed to be primarily responsible for the toughness enhancement of heterogeneous polymer systems through the addition of easily cavitating rubbery particles.