Physically meaningful and easy-to-use analytical solutions are obtained, using analytical modeling and theory-of-elasticity approach, for thermal stresses in typical through-silicon-via (TSV) packages of 3D IC devices. The case when the package is heated up from the room temperature to an elevated temperature is considered. Two extreme cases of the TSV geometry are addressed: disc-like vias, with height/thicknessto-diameter ratio is below 0.25, when plane-stress approximation in the 2D elasticity theory can be used, and rodlike vias, with height-to-diameter ratios above 2.5, when plane strain approximation is applicable. The following objectives have been pursued in the analysis: 1) evaluation of the elastic stability of a disc-like via subjected to the thermal "hoop" pressure caused by the thermal expansion mismatch of the copper (Cu) and silicon (Si) materials; 2) assessment of the thermally induced circumferential stresses in the Si wafer; and 3) the evaluation of the expected relief in the longitudinal (in the TSV axial direction) interfacial shearing stresses due to the application of a ''surrogate'' buffering material, i.e., a material not needed from the standpoint of the functional performance of the design. While the pressure at the Cu/Si interface determines the reliability of the Si material, the longitudinal interfacial shearing stress is critical from the standpoint of the adhesive and cohesive strength of the TSV structure. The numerical example is carried out for different radii of the opening in Si and for the case when Indium is considered as a suitable buffering material. The calculated data indicate that larger openings in Si result in lower pressures on Si and in lower longitudinal interfacial shearing stresses, especially if disc-like vias are employed. The computed data indicate particularly that a 1 m µ thick layer of Indium resultes in about 39% reduction in the induced pressure at the Cu/Si boundary for a disc-like TSV and by about 14% -for a rod-like via. As to the longitudinal interfacial shearing stress, the reductions are even greater: about 69% -for a disc-like TSV and about 41% for a rod-like via. Thus, there seems to be an incentive for employing disc-like TSV designs for lower thermal stresses. In the absence of the strain buffer, the pressure in the disc-like TSV design was only about 58% of the pressure in the rod-like via, and the maximum value of the longitudinal shearing stress was about half the stress in the rod-like TSV. The "bad news" is, however, that while the elastic stability of a rod-like via is never a problem, a disc-like via might buckle under the action of the thermally induced "hoop" stresses, and therefore the elastic stability of a disc-like via should always be evaluated and assured. Our analysis starts, for this reason, with the evaluation of the critical (Euler) pressure for a disc-like TSV.