This study aims at quantifying malfunctioning in the reciprocating compressor and establishing a new monitoring technique. We proposed a mathematical model (eleven degrees of freedom) in which deterioration and damage are expressed by changing model parameters. In addition, we can elucidate the cause of the resonance peak that occurs during operation by examining the frequency characteristics of the reciprocating compressor and the natural vibration characteristics by the use of numerical analysis. Then, we perform parameter identification using the natural frequency characteristics and examine the model parameter estimation method, which uses the relationship between the natural frequency characteristics and the frequency characteristics during operation. As a result, it was confirmed that the estimation method enables to express vibration characteristics using the error function about the natural frequency characteristics. In addition, it was possible to estimate the vibration characteristics by using the proposed model.