The invention relates to the design of turbine rotors which operate both as a pump and a motor and which are essentially made by joining two types of plates, namely a pressure plate and a suction plate, the shapes of which are based on the criterion of dynamic symmetry, whereby a theoretical dynamic symmetry surface (1) has a twisted shape, such that a current of fluid (2) can be conveyed along one of the faces thereof, following a pre-determined path and exerting thereon pre-determined stresses, while at the same time another current of fluid (3) can be conveyed along the other face thereof, following another path symmetrical to the first and exerting thereon other stresses symmetrical to the first. The invention provides different structural solutions that demonstrate the application of the criterion of dynamic symmetry to the design of radial, axial and mixed flow turbines.