The problem of thermocapillary convection in multiple immiscible liquid layers in a differentially heated shallow rectangular cavity with rigid and insulated upper and lower boundaries is considered. A three-layer system is considered as a model for multiple liquid layers. The middle layer is encapsulated on both sides by immiscible liquids, and features two interfaces which are considered to be deformable. The method of matched asymptotic expansions is used to determine the flow in the two distinct regions : the core region characterized by parallel flow; and the end-wall regions where flow turns around. Interfacial tension gradients induced by differential heating of the cavity drive the flow. Mechanical coupling across interfaces between immiscible liquids is investigated by varying the encapsulant viscosity and the height of encapsulant layers.