Rapid increase of refrigeration & air-conditioning system (r & a system) in modem industries brings attention to the urgency of research & development as a core technology in the area. And it is required to the compatibility problem of r & a system to alternative refrigerant for the protection of environment. Then, it is requested to study the lubrication characteristics of refrigerant compressor which is the core technology in the r & a system. The study of lubrication characteristics in the critical sliding component is essential for the design of refrigerant compressor. Therefore, theoretical investigation of the lubrication characteristics of rotary compressor for r & a system is studied. The Runge-Kutta method is used for the analysis of the behavior of rolling piston in the rotary compressor. The results show that the rotating speed of shaft and the discharge pressure have an important effect upon the angular velocity of the rolling piston. This results give important basic data for the further lubrication analysis and design of the rotary compressor.