On généralide les équations de Lagrange et le principe de Hamilton au cas du milieu continu anélastique. On exprime ensuite les principes de la thermodynamique en prenant en compte des discontinuités mobiles éventuelles. In classical mechanics of rigid solids or systems with finite number of degrees of freedom, the lagrange equations and the hamiltonian principle for conservative systems have been introduced. The propose of this note is to generalize these notion in continuum mechanics for anelastic systems. In the expressions obtained we take into account of moving discontinuities inside the continuum.