Acoustic emissions were recorded in the process of uniaxial compression of samples of various geomaterials. The experiments were carried out on a low-noise lever setup with water leakage; the maximum load on the sample did not exceed 250 kN. Some of the samples were tested at a continuously increasing load, the other at its stepwise change. The energy distribution of acoustic emission signals was investigated. The energy characteristic of acoustic emission was the square of the maximum signal amplitude. The flow of AE events is considered from the standpoint of nonequilibrium thermodynamics and Tsallis statistics. A decrease in the steepness of the linear part of the repeatability plots for a particular geomaterial was revealed when changing the loading mode from linear to stepwise, which means an increase in the proportion of higher-energy events with a stepwise change in load.