This article considers the development and research of a new design of crosshead-free piston hybrid power machine. After verification of a system of simplifying assumptions based on the fundamental laws of energy, mass, and motion conservation, as well as using the equation of state, mathematical models of the work processes of the compressor section, pump section, and liquid flow in a groove seal have been developed. In accordance with the patent for the invention, a prototype of a crosshead-free piston hybrid power machine (PHPM) was developed; it was equipped with the necessary measuring equipment and a stand for studying the prototype. Using the developed mathematical model, the physical picture of the ongoing work processes in the compressor and pump sections is considered, taking into account their interaction through a groove seal. Using the developed plan, a set of experimental studies was carried out with the main operational parameters of the crosshead-free PHPM: operating processes, temperature of the cylinder–piston group and integral parameters (supply coefficient of the compressor section, volumetric efficiency of the pump section, etc.). As a result of numerical and experimental studies, it was determined that this PHPM design has better cooling of the compressor section (decrease in temperature of the valve plate is from 10 to 15 K; decrease in temperature of intake air is from 6 to 8 K, as well as there is increase in compressor and pump section efficiency up to 5%).