Cryogenic piston pumps are commonly found in cryogenic systems to pressurize low-temperature liquefied fuels, such as liquified natural gas (LNG) or hydrogen, which are then gasified and stored in high-pressure vessels. The main challenges to be tackled in the design of these machines concern the low operating temperatures, high discharge pressures, and especially the need to avoid liquid evaporation, as this can lead to a reduction of volumetric efficiency or even to the shutdown of the pump. Two effects can cause the formation of vapor bubbles: cavitation, i.e., when the static pressure falls below the saturation value during the suction phase, and evaporation due to a temperature increase of the cryogenic liquid.In this study, a numerical analysis of a cryogenic single-piston pump is carried out. In the first part of the activity, the suction phase is studied through three-dimensional, steady-state CFD simulations. The performance of the pump in terms of pressure losses is evaluated and possible improvements to the suction geometry are identified.Then, two-phase steady-state Eulerian-Eulerian simulations are performed. The Rayleigh-Plesset model is used in order to evaluate the onset of cavitation. The minimum inlet pressure conditions that avoid cavitation are identified for two different geometries underlining the positive effect of the introduced modifications. Results show that the methodology applied in this work can lead to improvements in cryogenic pump design, reducing the static pressure losses and hence limiting the risk of cavitation.