A stress analysis model is developed to assess the stresses in solder joints caused by thermal contraction mismatch between a low expansion flex-circuit (FC) and a high expansion rigid substrate. It is shown that application of low expansion FCs can result in significant stress relief for solder joints. This is due to the fact that the force acting on a joint cannot exceed the buckling force for the adjacent portion of the FC. It is shown that the strains in solder joints interconnecting FCs to rigid substrates can be made very small, thereby resulting in a substantially longer fatigue life of the interconnection. In the executed example these strains are about two orders of magnitude smaller, than in the case of a rigid board. The obtained results can be utilized as guidance in physical design of assemblies with FCs.