[en] Recent experiments on polycrystalline materials show that microcrystalline materials have a strong dependency ona grain size. In this study, mechanical and electrical properties of polycrystalline materials in micro level were studied by using averaging theorems. To completely understand the size-dependency of polycrystalline materials, an integral non-local approach that can predict the stress-strain relations for these materials was presented. In microcrystalline materials, crystalline and grain-boundary were considered as two separate phases. Mechanical properties of the crystalline phase were modelled using crystalline brittle material and is composed of randomly distributed and orientated single crystal anisotropic elastic grains. For microcrystalline materials, the surface-to-volume ratio of the grain boundaries is low enough to ignore its contribution to the elastic deformation. Therefore, the grain boundary phase was not considered in microcrystalline materials and mechanical properties of the crystalline phase were modelled using appropriate integral non-local approach. Finally, the constitutive equations for polycrystalline materials were implemented into a boundary integral equation and the results and some examples are provided for piezoelectric ceramic. (paper)