Surface-plasmon polaritons (SPPs) existing at metal-dielectric interfaces with exponentially damped vertical intensity profiles have attracted much interest for their capability of confining light energy into a small space beyond the diffraction limit. Theoretical considerations have been given to understandings of wave behaviors based on Maxwell's equations taking into account metals as dielectric materials with negative permittivity. However, since this approach assumes metals as homogeneous media, it is difficult to perform detailed analysis on propagation mechanisms in three-dimensional micro and nano structures. Here we propose a theoretical method based on the dynamics of electric dipoles formed by local displacement of free electrons in metals to describe SPP waves. In this method, the Poisson equation is used to describe actual movement of electrons in metals interacting with the electromagnetic field. Based on this method, we have revealed fundamental properties including electron density distribution functions in the area close to metal surfaces, SPP waves are then modeled by reconstructing microscopic features of such novel electromagnetic waves in a given material systems. After this simple verification, we make the best use of this method to explain SPP propagation at ultra-thin metal films or along narrow metal wires.