Zirconium alloys are widely used as structural materials in the core of nuclear reactors. In such conditions, the continuous exposure to neutron irradiation of these alloys can have considerable effects on their microstructure and mechanical properties, which significantly impact their overall performance. In this work, we investigate the cumulative effects of irradiation damage in $\alpha$-Zr using molecular dynamics (MD) simulations. To this end, displacement cascades are approximated using the computationally efficient stochastic core–shell model. Application of this approach results in structural damage which is representative of those generated using the more computationally demanding simulations of explicit collision cascades. Therefore, the examination of the damage at the atomic-scale, and the effects of long-term irradiation exposure on the material properties of zirconium can be assessed. We first evaluate the influence of radiation damage on the mechanical response of single crystal $\alpha$-Zr. Subsequently, the effects in $\alpha$-Zr systems including symmetric tilt grain boundaries are investigated.