Localized states of discrete structures play an important role in energy transfer and reduction of potential barriers for local structure transformation. In this paper, we consider the influence of the surface curvature of the crystal with  cylindrical symmetry on the possibility of excitation of surface localized modes. The study is performed by means of molecular dynamics method. A face-centered cubic crystal of composition A3B with an L12 superstructure, where component A is Pt, B is Al is considered. The interaction of particles was described by the interatomic potential obtained by the embedded atom method. We demonstrate the fundamental possibility of the existence of localized modes  on the surface under consideration. External oscillations, in turn, can imitate the boundary conditions corresponding to the dynamics of the crystal volume, thereby leading to the consideration of modes located far from the  surface. The energy and dynamic characteristics of localized excitations are calculated as functions of the curvature and location of the atom on the crystal surface.