This paper deals with the invariance of the mechanical system with rhe-onomious constraints. Hamilton function is suggested to be in form (20). In such a case invariance is proved by the relations (33) to (36). That implies another approach to the kinetic potential (19). The strength of the rate of change of the rheonomous constraints is introduced. Such an approach modifies Hamilton’s and D’Alambert’s principles for preserving their invariance. The approach theoretically proved is illustrated with a few examples.