The elastic deformation due to time dependent surface traction (from the Duhamel-Neumann Analysis) can be determined without reference to its Thermal State. This procedure is adopted in the solution of the dynamical problem in classical theory of elasticity. The elastic constants which Appear in the equations of motion are defined under adiabatic conditions and since elastic waves being non dispersive, produce no increase in the entropy of the solid. No inconsistency seems to arise. This discription of elastic wave propagation is physically over simplified. In fact a change in volume must cause the temperature as well as the stresses to change. Coupled thermo-elastic wave problem concerning the region outside a circular cavity in a homogeneous and isotropic elastic media under mechanical blast loadings as special case has been considered. The expressions for stresses and temperature are obtained.

Keywords: Elasticity, Thermo-Elastic, Isotropic Elastic, Oscilation.