The modern age of industry, machines, household needs and other everyday life represent great demands and a wide range of needs for hydraulic systems, hydraulic machines and the piston pumps. In order for the advancement of hydraulic systems and piston pumps to be successful for use, appropriate system parts, appropriate fluids of a certain viscosity, construction, flow calculation, system dimension calculation, pump power calculation and more are required. The paper analyzes the working fluids and influences, describes the types of flows that play an important role in the proper functioning of the hydraulic system and the pump piston, the losses of the pipeline and the principle of operation of hydraulic (dynamic) pumps. Designs of piston pumps (single-acting, double-acting, differential), components and area of application are described. The paper describes the problem task, the calculation of the hydraulic system from a single-acting pump with two cylinders, where the difference of hydraulic losses before and after the reconstruction of the system is seen. Every element, parameter and calculation is essential for the hydraulic system and the piston pump itself to perform successfully without any possible difficulties.