An experimental study has been conducted on natural materials such as sandstone and andesite, which are commonly used in the mining, oil and gas industries, as well as in road construction. Cylindrical samples were tested under quasi-static and dynamic loads in fragment preservation conditions. X-ray tomography was used to determine the stages and mechanisms of destruction and the spread of cracks in the material before and after testing. The quasi-static uniaxial compression tests were performed, in which the deformation fields were measured, in situ, by using the digital image correlation method and acoustic emission signals. Analysis of the results revealed the specific features of fracture of andesite and sandstone samples. The destruction of andesite, which consists of hard and soft phases, follows a quasi-brittle scenario in the soft phase, with the size of the resulting fragments corresponding to the solid phase. When main vertical cracks spread throughout the entire volume of sandstone, which is a homogeneous material and consists of strong, loosely interconnected grains of sand, there was no sharp drop in its bearing capacity because friction forces between sand grains contribute significantly to holding them together, especially under compression conditions. Once the load was taken off, the sample broke up into pieces. The destruction of the tested samples subjected to quasi-static loading proceeds in two steps. The first step involves the accumulation of damages in the form of multiple main cracks coinciding with the direction of the maximum stress. During the second step, multiple daughter cracks are formed, which promotes the failure of the sample. In the case of dynamic compression, complete fragmentation of the sample occurred when the energy of the loading pulse was sufficient, and this was accompanied by the separation of the formed fragments. The results of this study are promising for the development of numerical fracture models intended to investigate the kinetics of defect nucleation and growth in rocks. These models can also be used to optimize the drilling processes.