The mathematical model for calculating the response time of the compression ratio of the mechanism for compression ratio changing (MCRC) is presented in this article. This revealed the influence of various engine factors with the connecting rod and crank mechanism (CRCM) on the operation of the MCRC (for example, the rate of the compression ratio change). The results of the study of the operation of the MCRC indicate a strong influence of the values (relative area of flow passage of channels) and р (pressure) on the response time τ in the field of their small values. This indicates that with insignificant changes of the area of flow passage of channel of the hydraulic lock and the minute oil pressure in the cavities, a significant response rate of the MCRC is ensured. The results demonstrate the possibility of speedy compression ratio change in the engine with the MCRC. Calculation studies showed that the mechanism full operation occurs quickly (0.02 s per unit εx), which indicates the expediency of using such a high-pressure pump in a four-stroke gasoline engine with CRCM. The mechanism movable body complete movement (S = 4 mm) at the oil temperature in the hydraulic system of 45°C and pressure on the body of p = 60 bar are stated to occur for 0.2 s.