Surface plasmon polaritons (SPPs) on a curved metal–dielectric interface are shown to experience a geometric potential Vtop like quantum particles confined on a curved surface. As opposed to electrons or photons constrained by a squeezing potential, no ambiguities arise in the definition of the geometric potential for SPPs. A general form of Vtop for SPPs on a generalized cylindrical surface is derived by a multiple-scale asymptotic analysis of vectorial Maxwell's equations for the case of a curvature radius larger than the SPP wavelength.