A hydraulic support is one of the most important pieces of equipment in fully mechanized coal mining, and its stability and reliability will have a direct impact on fully mechanized coal mining. In order to deeply elucidate the dynamic working characteristics of a hydraulic support during lifting, lowering, and moving, and to provide theoretical support for further optimizing the stability and reliability of a hydraulic support, the dynamic characteristics of a hydraulic support are studied in this paper. Firstly, in order to study the dynamic working characteristics of hydraulic support lifting, a rigid–flexible coupling dynamic simulation model of a hydraulic support is established; in order to study the dynamic working characteristics of hydraulic support moving, a microcontact dynamic model of a hydraulic support and the caving face roof and floor based on G-W contact theory is proposed, and the first rigid–flexible–mechanical–hydraulic coupling dynamic simulation system of a hydraulic support and the roof and floor of a caving face is established in the industry. Then, based on this foundation, simulation experiments are conducted for hydraulic support lifting, moving without pressure, and moving with pressure, respectively. The working characteristic parameters of the hydraulic support are collected and analyzed. The results show that working speed, working height, surface contact conditions, residual working resistance, and impact load have different effects on the stability and reliability of the hydraulic support. This study can provide in-depth technical support and theoretical guidance for understanding and improving the dynamic working characteristics of the hydraulic support.