In this work, the invariance conditions of the Lagrangian function (or the action integral) are discussed in terms of the assumed transformation groups that lead to the corresponding conservation laws. The conservation laws obtained in the general form were applied to the problems of thermoelastic membranes and the corresponding laws were derived from them. It should be noted that one of the laws obtained represents the generalization of the well-known J-integral in thermoelastic membrane theory. It is also pointed out that in the absence of temperature the same law is derived for the orbit-independent integral that Lo [7] obtained for the elastic membranes.