In order to combine the merits of epoxies, which provide good environmental and mechanical protection, and the merits of silicone gels, resulting in low stresses, one can use an encapsulation version, where a low modulus gel is utilized as a major encapsulant, while epoxy is applied as a protecting cap. Such an encapsulation version is currently under consideration, parallel with a metal cap version, for the Advanced VLSI package design which is being developed at AT&T Bell Laboratories. We recommend that the coefficient of thermal expansion for the epoxy be somewhat smaller than the coefficient of thermal expansion for the supporting frame. In this case the thermally induced displacements would result in a desirable tightness in the cap/frame interface. This paper is aimed at the assessment of stresses, which could arise in the supporting frame and in the epoxy cap at low temperatures. Also, the elastic stability of the cap, subjected to compression, is evaluated. The calculations were executed for the Advanced VLSI package design and for a Solder Test Vehicle (STV), which is currently used to obtain preliminary information regarding the performance of the candidate encapsulants. It is concluded that in order to avoid buckling of the cap, the latter should not be thinner than 15 mils (0.40 mm) in the case of VLSI package design and than 17.5 mils (0.45 mm) in the case of STV. At the same time, the thickness of the cap should not be greater than necessary, both for smaller stresses in the cap and for sufficient undercap space, required for wirebond encapsulation. The obtained formulas enable one to evaluate the actual and the buckling stresses. Preliminary test data, obtained by using STV samples, confirmed the feasibility of the application of an epoxy cap in a flip-chip package design.