The shape of irradiation-induced void at high temperatures and irradiation doses in metal materials is usually the complex-shaped polyhedron, to strongly affect the mechanical properties and service performances. Here, considering the three-dimensional geometric configuration of polyhedron void, we develop a model to calculate critical resolved shear stress for the interaction between dislocation and polyhedral void. This model can be used into the crystal plasticity theoretical framework, to predict the void-shape-dependent hardening behavior under different irradiation doses, times, and temperatures in the irradiated face-centered-cubic metals. The effect of the spatial interaction between polyhedron void and sliding dislocation has been considered by a probability-dependent void-strengthening mechanism, for the accurate prediction of the yield stress. The feasibility is verified by comparing the experimental data of the irradiated polycrystalline Cu and irradiated 304 stainless steel with the numerical result calculated from the current model. The contribution of cubic void on hardening is higher than that of octahedral and cuboctahedral voids, owing to the difference of the cross-sectional shape caused by the dislocation-bypassing-void process, where the triangle section provides a higher critical resolved shear stress than the hexagon section. The hardening contribution of the cubic void increases firstly, and then decreases with the increasing void volume fraction, revealing the hardening-to-softening transformation. In the irradiated polycrystalline Ni, the yield stress increases with increasing radiation dose and time, and decreases with increasing irradiation temperature, to provide the accurate irradiation hardening predictions. The current model establishes a theoretical approach to capture the hardening behavior in the irradiated metals containing polyhedron void, for predicting the yield strength of metal materials under the changeable irradiated environments. (C) 2020 Elsevier B.V. All rights reserved.