Analytical models are developed to estimate the transient elastic response of cooling two-layer solid cylinders with different end and boundary conditions. Such cylinders contain two layers that are in perfect contact. The hot assembly loses energy from its surface to either zero ambient by convection or by a prescribed lower surface temperature. In any case, as the cooling takes place slowly, the problem is amenable to use of the uncoupled theory of elasticity. A generalized plane strain solution is derived and then reduced to the state of plane strain by simply setting the axial strain equal to zero. The results of these solutions revealed that the radial and circumferential stresses remain unchanged by end conditions when the boundaries are free. However, in case of plane strain, the axial stress becomes the dominant stress component and it is much larger than that in free ends. Radially constrained boundaries create very large stresses in the assembly but the corresponding stress state is far away from yielding