Pneumatic driven high pressure pumps (PDHPPs), having a number of considerable advantages in comparison to other types of high pressure pumps, are widely used in different sectors of modern industry. However, estimating the performance characteristics of a PDHPP is complicated due to the specifics of physical processes taking place during its operation. A mathematical model was developed to solve this problem. Two main operating modes are considered: for constant load and for constant volume, which cover the most common uses of the PDHPPs. The solution of the model made it possible to estimate how various parameters affect the operation of the pump. Thus, with an increasing pressure of compressed air, the volume flow grows at the pump outlet; with a higher pressure of the pumped liquid due to compressibility and a higher load on the drive cylinder, the flow, on the contrary, reduces. In case the PDHPP operates for the constant volume, the time of pressure increase grows with an increase of the required pressure and the value of this volume. The mathematical model and computational data can be used in the development of new and modification of the existing pumps.