The article presents a mathematical model of a double-acting free-piston generator developed based on the Lifan 188F engine. Various types of free-piston generators (FPG) are considered, with a focus on a single-piston double-acting design where each stroke is a working stroke. A simplified mathematical model is presented, including piston dynamics, gas and electromagnetic forces, as well as friction force. Simulation results indicate that the average piston speed is 6.4 m/s, which is approximately 2 times lower than in the Lifan 188F engine with similar characteristics. Based on calculations, an FPG prototype has been developed using ring magnetic cores and a simplified air scavenging system. The developed generator is expected to have a 10 kW-scale power output and dimensions of 610 mm in length and 108 mm in diameter, providing a lower center of gravity. The design includes an air cushion to soften the piston stroke and enhance operational safety. The developed mathematical model allows for the evaluation of the characteristics of the designed generator and confirms the absence of risk of piston collision during stable operation.