In this paper the mathematical models of the main types of turning hydraulic engines, which at the present time widely used in the construction of handling systems of domestic and foreign mobile transport-technological machines wide functionality. They allow to take into consideration the most significant from the viewpoint of ensuring high technical-economic indicators of hydraulic efficiency criteria – minimum mass (weight), their volume and losses of power. On the basis of these mathematical models the problem of multicriterial constrained optimization of the constructive sizes of turning hydraulic engines are subject to complex constructive, strength and deformation limits. It allows you to develop the hydraulic engines in an optimized design which is required for the purpose of designing a comprehensive measure takes into account efficiency criteria. The multicriterial optimization problem is universal in nature, so when designing a turning hydraulic engines allows for one-, two — and three-criteria optimization without making any changes in the solution algorithm. This is a significant advantage for the development of universal software for the automation of design of mobile transport-technological machines.