Plasmon is considered to be the incompressible self-oscillation of conducting electrons in small nanoparticles. A classical spring model could be used to describe plasmon’s behavior. Many different techniques have been applied to understand nanostructure’s plasmonic properties. Electron energy loss spectroscopy (EELS) is one of these tools, which is helpful for us to understand the interaction between fast moving electrons and nanomaterials. It could achieve very high spatial and energy resolution. Here, we develop a new finite-difference time-domain method to calculate EELS spectra and maps, which is based on a commercial software package “Lumerical”. The calculated results for different cases are compared with the well-known boundary element method (BEM) and show an excellent agreement. Our finite-difference time-domain (FDTD) method to calculate EELS spectra has further been proven really helpful by high-density plasmonic dimers’ experimental results. There are basically two different numerical techniques. One is based on finite difference method (FEM) and another is according to finite-difference time-domain method (FDTD). Both of them are very important to perform optical calculations in nanophotonics and plasmonics area. In general, they will try to solve Maxwell equations with many different boundary conditions numerically. Optical properties of nanomaterials are also very tremendous for us to understand plasmonics behavior in the external electromagnetic fields. We systematically performed FEM simulations for different dimensions’ split ring structure and identified each plasmon mode via induced charge plot. Later we also studied hollow Au Nanoshells: hollow Au-Ag Nanoshell and hollow Au-Co Nanoshell. The former showed the surprising in vivo instability in the near infrared region while the later has potential application in hot electron generation.