The Constrained System whose motion may be described in terms of non.independent State functions.The Lagrangians and Constraint Condit. ions may be involving hiqh-order derivatives.Suppose the action integral and the Constraint Condition are invariant under the Symmetry transform. ation of the tim-space Coordinites and the state function.Then.We Can generalize the Noether's theorem to this Constrained System.In general.It does not yields the Conservatou Lws as Classical Noether's theorem.The translaton invariance and Lorentz invariance yield generalization Conserv. ation of energy-momentum and angular momentum.However

If the System only Subject to a finite Constraint

It does not reduce to the Conservation Law as the non-Constraint

System But if the System Subzect to such Co. nstrint

under the internal Symmetry transformations the generalization Noether's theorem reduce to the results as the non-constraint System.The generalization Cortservation of energy-momentum are equivaleut to the Euler—Lagrange equations of the Constraint System.Our general resnlts may be application to incompressible Continuous media.