Optical properties of nanoparticles are related to their surface plasmon resonance. In this work, we use Mie theory to compute the extinction, absorption, and scattering properties of noble metal nanoparticles. The calculated results agree well with the experimental values. With increasing particle size, particle dipole absorption peak will be red-shifted; and the peak position and the size of the nanoparticles have a linear relationship. It is found that the ratio of core to shell size determines the absorption properties of spherical Au/Ag core/shell nanoparticles. When the Au shell is thin, the optical properties vary with the adjustable shell. When the Au shell is thick, its optical properties are similar to the pure Au nanoparticle. Through the calculation and analysis we made, the Mie theory can be generalized to nanocavity structures when the shell thickness reaches a certain value. Furthermore, it is found that the absorption peaks of alloy nanoparticles have a linear relationship with the alloy composition.