We present a new multi-scale numerical methodology to estimate of elastic properties of core samples. This approach combines the geostatistics to estimate distribution of effective cementing material, computational topology for automatic grain detection, and numerical upscaling. The main idea of the approach is to start from the microscopic images and finely-resolved CT-scans to estimate distribution of the grain surface roughness, distance between grins, and cementing material. After that using numerical upscaling generate distribution effective properties of cement but for the model with flat grain-to-grain contacts. At the last step we embed the effective cement into a mid-scale CT-scans, where grins are represented as convex polyhedrons obtained by means of computational topology.