Abstract Assessment of effective mechanical properties such as elastic properties and brittleness can be challenging in the presence of complex rock composition, pore structure, and spatial distribution of minerals, especially in the absence of acoustic measurements. Conventional methods such as effective medium modeling, are not reliable for assessments of mechanical properties in complex formations such as carbonates, because solid skeleton of carbonates does not consist of granular minerals with ideal shapes. The effective medium models also overlook both the spatial distribution of petrophysical properties, and the coupled hydraulic and mechanical (HM) processes, which causes significant uncertainties in geomechanical evaluations. The objective of this paper is to develop a numerical method to enhance assessment of effective mechanical properties of anisotropic and heterogenous carbonate formations by modeling the variation of effective stress and the evolution of corresponding strain. The developed method takes into account the coupled HM processes, the realistic spatial distribution of rock inclusions (i.e., rock fabrics), dynamic fluid flow, pore pressure, and pore structure. To achieve this objective, we develop a pore-scale numerical simulator by satisfying conservation equations and considering the coupling among relevant HM phenomena. We adopt peridynamic theory to discretize the micro-scale medium. The inputs to our numerical modeling include pore-scale images of rock samples as well as mechanical and hydraulic properties of each rock inclusion. We perform image processing on micro-CT scan images of rock samples to obtain a realistic micro-scale structure of both rock matrix (i.e., concentration, spatial distribution, and shape of rock constituents) and pore space. We then assign realistic mechanical and hydraulic properties to each rock constituent within the pore-scale medium. The outcomes of numerical modeling include the variation of effective stress and the evolution of corresponding strain by honoring the variability in mechanical/hydraulic properties of rock inclusions caused by their spatial distribution, pore pressure, pore structure, natural fractures, and dynamic fluid flow at the micro-scale domain. We then compare the outcomes of numerical models with the mechanical properties estimated based on effective medium models.