This paper describes the issues and calculated the performance of the heart pumps. The introductory chapter describes the general problems of modern society related to heart disease and a growing need for cardiac pumps that will support the heart, or completely replaced it. The first chapter describes the blood and its characteristics, as well as problems related to blood. It also describes mechanisms of hemolysis and thrombosis, which are based on defined criteria for the operation of the pump (permissible area of the shear stress and damage index of red blood cells). The second chapter describes the heart and how it works. Heart pumps that are used in practice are also analyzed in this chapter. Further in this work working fieldof heart pump is defined based on physiological data related to the actual heart. For two types of friction pumps: cylindrical friction pump and friction pump with rotating disc are derived by analytical expressions that connect the growth pressure and flow through the pump, define the power required to drive the pump, the minimum and maximum shear stress, efficiency pump and damage index of red blood cells. There are two types of diagrams defined: one that is used for selection of the pump (size and speed), and the second to analyze the characteristics of the selected pump (of selected dimensions) in the default working field. Comparing the two pump types it was found that pump with a rotating disc was favorable, but it would be necessary to check this conclusion with complete numerical solution of the Navier-Stokes equations for the flow through the two pumps, since the used analytical solution of a pump with a rotating disc is probably physically unrealistic, because of the introduction of assumptions that was necessary to find a solution.