The problem of convective flow in multiple immiscible liquid layers in a differentially heated shallow rectangular cavity with rigid and insulated upper and lower boundaries is considered. As a model for multiple layers, a three-layer system featuring two non-deformable interfaces is investigated. 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. The driving mechanism for convection is buoyancy. To study mechanical coupling across interfaces between immiscible liquids, the influence of varying encapsulant viscosity is investigated.