We consider the system of a quantum well embedded in a planar semiconductor microcavity with a shallow circular mesa patterned on top of the cavity spacer. For this system we develop the linear coupling theory of polaritons. We then compute polariton eigenstates and the corresponding optical spectrum. The theory predicts the existence of laterally confined polariton states with a discrete energy spectrum, as well as continuum states above the finite mesa potential barrier. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.