The increased need for water pumping, especially for domestic use in remote places, together with the accelerated rise of fuel costs, brought about the development of solar powered electric water pumps (SPEWP). The SPEWP consists of a solar cell array, storage of electrical energy or water, controls, an electric motor and a pump. This paper deals with the characteristics of each element in a spewp and its mathematical model. The mathematical model of the whole system is studied and analysed. The solutions of the non-linear equations yield a method for determination of the rate of volume flow, the head of water and the efficiency of the system as a function of the radiation levels. The pump motor is studied and so is its operation point and the torque under varying conditions of the load and the solar energy available. A numerical solution of the mathematical equation is presented describing the torque of the series d.c. motor as a function of its characteristics and the non-linear nature of the solar cell array (SCA). The centrifugal pump operation is analyzed by the torque equation and its variations as a function of the pumped rate of flow and the rotation velocity is studied. A method for determination of the pump parameters is given. Finally, we discuss the principles and method for obtaining the rate of volume flow and the head of water as a function of the radiation levels. The theoretical results are compared to measured ones allowing us to examine the validity of correction factors. The authors believe that this paper contributes to better design of SPEWPs, which, in many cases, even without improvements are being chosen today over conventional water pumping systems.