A multi-chip module (MCM) structure comprises more than one semiconductor chip lying in a horizontal plane, the MCM having individual chip contact patches on the chips and a flexible heat sink having lateral compliance and extending in a plane in the MCM and secured in a heat exchange relation to the chips through the contact patches. The MCM has a mismatch between the coefficient of thermal expansion of the heat sink and the MCM and also has chip tilt and chip height mismatches. The flexible heat sink with lateral compliance minimizes or eliminates shear stress and shear strain developed in the horizontal direction at the interface between the heat sink and the chip contact patches by allowing for horizontal expansion and contraction of the heat sink relative to the MCM without moving the individual chip contact patches in a horizontal direction.