Nanostructures have received much attention from the physical and engineering communities in the past few years. The understanding of the behavior of nanostructures in various conditions is warranted since the applications of such materials in optics, electronics, and mechanics is ever expanding. This thesis investigates a specific type of structure, a concentric cylindrical. More specifically, the dispersion relation of radiating and non-radiating plasmon polaritons (quasi-particles resulting from interactions of photons and surface electrons) is studied under varying conditions. We intend to show the influence of changing the thickness of the layers, the number of layers, the curvature of each layer, and the type of material the layers has on the dispersion relation. By first solving Maxwell's equations in cylindrical coordinates and applying boundary conditions, we developed a matrix equation through which we were able to obtain the dispersion relation for an N layered cylindrical system characterized by a specified dielectric function placed into a background. For the non-radiative modes we used the bisection method to obtain the dispersion relation; however, since radiative modes encompass virtual modes, which contain real and imaginary components, a Newton method was used to gather that data. The dielectric functions for silver and carbon dielectric functions were used to describe the material layers within the radiative and non-radiative regimes. The results show that curvature changes influence the surface plasmon polariton dispersion by either red shifting or blue shifting the energetics. Lifetimes and damping are seen to be influenced by the curvature as well. The addition of more layers to the system results in an increase in the complexity of the dispersion energetics. The results obtained would help provide better scanning tips within the optical microscopy field. Also, these results can have direct application to the field of photonics. Finally, these results also help provide the foundations to understanding the fundamentals of long-ranged forces in cylindrical layered structures.