Abstract: The fundamental equations in finite element method for unsteady temperature field elastic plane proble m are derived on the bases of variational principle of coupled thermoelastic problems,In these derivations,elastic plane is divided into three nodes triangular elements,and time interval is divided into linear time elements,in which all the variables,including displacements and temperatures at various nodal points,are varied linearly with time,Two coupled sets of linear algebraic equations of all the unknown displacements and temperatures at every nodal point in every instant(i,e,the terminal values of time elements) are obtained.They are the fundamental equations of the said problem.