The dynamic free response of thin rectangular plates subjected to one and two dimensional steady state temperature distributions satisfying Laplace's equation is analyzed. The governing equations of motionare derived by a finite difference method and solved by a simultaneous iteration technique to obtain eigenvalues and eigenvectors. The accuracy of the method is assessed by comparing the results for some typical cases with those obtained by classical methods. The finite element method is also employed for the problem and the results obtained compare well with those of the finite difference method. From the results an attempt is made to correlate the non-dimensional frequency parameter and the temperature. Plates of different boundary conditions, with at least one edge clamped, free to expand or contract in their planes, are studied. © 1978 Academic Press Inc.