In this study, a procedure for estimating Young's modulus of textured and non-textured polycrystalline materials was examined based on finite element analyses, which were performed using three-dimensional polycrystalline finite element models of a random structure, generated using the Voronoi tessellation. Firstly, the local stress/strain distribution and its influence on macroscopic elastic properties were evaluated. Then, the statistical relationship between Young's modulus obtained from the finite element analyses and averaged Young's modulus of all grains evaluated based on Voigt's or Reuss' model was investigated. It was revealed that the local stress/strain in the polycrystalline body is affected by crystal orientation and deformation constraint caused by adjacent grains, whereas only the crystal orientation affects Young's modulus of the polycrystalline body when the number of grains is large enough. It was also shown that Young's modulus correlates well with the averaged Young's modulus of all grains, in which the size of grains is considered in the averaging. Finally, a procedure for estimating Young's modulus of textured and non-textured materials was proposed. Young's modulus of various materials can be estimated from the elastic constants of single crystal and the distribution of crystal orientation and size of grains, which can be obtained by using electron backscatter diffraction (EBSD).