We develop a depositional model that reconstructs numerically the geometrical structure and mechanical properties of natural sedimentary rocks in two and three dimensions. Our emphasis is on unconsolidated sands and sandstones. Our model has the following distinctive features: (1) it accounts for the dynamic geologic processes of grain sedimentation and compaction, and the diagenetic rock transformations; and (2) it reproduces the mechanical rock properties. The main input parameters are the grain size distribution, the final rock porosity, the type and amount of cement and clay minerals, the coefficient of friction, the bond strength parameters, and the grain stiffness moduli. The initial grain shapes are circular in 2D and spherical in 3D. Our depositional model can also be used to study the initiation, growth, and coalescence of micro-cracks in the rock. The proposed approach makes it possible to model the accumulation of rock damage and fracture propagation. The development of micro-cracks in, for example, a 2D marble rock model is studied under increasing vertical stress. Both the box fractal dimension of the micro-crack distribution and its variation with the applied stress are estimated.