In this paper, an automatic unstructured focused ion beam (FIB) and scanning electron microscopy (SEM) images induced representative volume element (RVE) finite element (FE) method is developed to predict submicron scale carbonate rock effective Young's and bulk moduli and Poisson's ratio on parallel CPU-GPU platform. Based on high resolution-contrast surface morphology and internal fabric-texture structure images from carbonate rock specimen (covered 0.12-64 mu m(2) area and 8000 mu m(3) domain), the cubic RVE FE models are constructed from different sites through Avizo with user-defined parameters Matlab coding. The effective Young's and bulk moduli and Poisson's ratio of the different RVEs and porosity and pore size are computed by using periodic boundary condition in the well-known FE software Abaqus. FE mesh sensitivity analysis has been conducted where all moduli converge to a certain constant value at larger FE mesh density. The effect of fabric-texture (pore size, shape, and distribution) on the elastic properties is discussed. The correlations between the computed effective elastic properties and pore size, porosity, RVE size have been established. The simulation results show that the effective Young's and bulk moduli and Poisson's ratio have strong anisotropic behavior and depend on RVE size, porosity and pore size. The RVE size, porosity and pore size are three independent factors in affecting of the effective elastic moduli, the effect mechanism of porosity and pore size is same while the effect mechanism of RVE size is difference.