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Based on an approximate method by the authors for calculating void deformation in crystalline solids, the global response of a small continuum material element which contains microcavities is studied. A rate‐dependent power‐law plastic flow by double‐slip is assumed to govern the local inelastic deformation. The local field variables are analytically calculated in an incremental manner. The average stress and strain are then computed by the integration of the local stress and strain over the continuum element. These average variables are used to describe the overall response of the material element under high loading rates. Several illustrative examples are given. It is shown that the global response of the material is significantly affected by the loading rate: the material response becomes tougher as the loading rate increases, but once the entire matrix becomes plastic, a strong ductility develops. It is observed that the large overall plastic deformation of crystalline solids stems not only from a uniform plastic flow in the entire matrix but also from the slip caused by the stress concentration near cavities; even under all‐around uniform compression or tension, significant plastic deformations can take place in the vicinity of preexisting cavities, and affect the overall response of the material. The global material response, in general, is anisotropic, being induced by local flow on geometric slip systems. In addition, it is shown that the overall material response under compression is not, in general, the reverse of that under tension. The overall failure of crystalline solids, caused by void collapse or void growth, is investigated under compressive and tensile loads applied at various rates.