Most high-pressure fuel pumps for compression-ignition engines manufactured today are cam driven. These pumps have numerous advantages, such as low energy consumption and limited production costs. However, a problem arising from the nature of the cam mechanism is an unfavorable distribution of forces in the camshaft-plunger-cylinder system of a delivery section. The authors have proposed an innovative pump design that eliminates most of the problems present in conventional solutions. The pump utilizes a gear-based hypocycloid drive. This paper focuses mainly on the strength analysis of the two critical components (countershaft and mount) of the subassembly under the highest load -simulations were carried out for different critical load states. The following procedure of estimating fatigue life was adopted for computations: the operational evolution of stresses will be systematized to the set of amplitude stresses and mean stresses by means of the "Rainflow" method. The results obtained in the work showed that the main factor determining change of stresses was the presence of clearances in the pump mechanism. It has been proved that the values of clearances have a negative influence on the power transmission in particular -their presence results in loads being carried by the countershaft and not by the support inter-operating with it. This may cause frictional wear of teeth, leading to the improper operation of the transmission. The analysis showed that the mount was designed correctly. This facilitates the use of less demanding constructional materials.