On the basis of the fundamental equations of thermodynamics, a new method proposed in this paper gives comprehensive consideration of the various factors, such as heat transfer, leakage, gas pulsation and valve motion, that influence the working process of the compressor and establish all the mathematical simulation equations. By using numerical computation, the thermodynamic parameters which govern the working process of the compressor and the macroscopic thermodynamic performances, such as capacity, power and specific power in the compressor can be found. The results of the computation are in good agreement with practical measurements and the correctness and applicability of the proposed method are demonstrated.NOTATIONA v flow area of valve gap, m 2 a p flow area of valve seat, m 2 F p piston area, m 2 H displacement of valve plate, mH 0 pre-compression value of spring, mh enthalpy, J kg - 1 M v valve plate mass, kgm gas mass, kgp pressure, N m - 2 Q heat transfer, JR gas constant, J(kg K) - 1 S piston stroke, mT temperature, Kv specific volume, m 3 kg - 1 W work, JZ p spring stiffness, N m - 1 Greek lettersα heat exchange coefficient, J(m 2 K) - 1 α v flow coefficient in valve gapβ lift force coefficient of valveθ crank angle, rad\ ratio of crank throw to length of connecting rodω angular velocity of crank, rad s - 1 Subscriptsc inside cylinderd dischargeli leak insidelo leak outsides suction