The thermodynamics of in-cylinder processes of the internal combustion engine in cranking mode when measuring compression were examined. Analysis of various theoretical models and comparison of known data showed that the problems of constructing mathematical models of the engine operating cycle remain unresolved. The vast majority of practical data and recommendations for measuring cylinder compression are based on empirical knowledge, numerous experiments and tests. In accordance with this, there is a need for computational models of the compression measurement process and their theoretical justification. To solve the identified problems, a mathematical model of the thermodynamic processes in the cylinder was developed. Unlike existing ones, the model describes the processes in the cylinder step by step, taking into account the real nature of the intake-exhaust processes, air leakage through the interfaces of parts and heat exchange with the walls. Using modeling, the main patterns of changes in compression depending on the modes, the nature of damage to the associated parts of the valve mechanism and cylinder-piston group, the amount of leakage and engine temperature were found. Based on the results of the study, the properties of the model which make its use effective in diagnosing and monitoring the technical condition of engines in operation were concluded.