This thesis examines theoretical methods for modeling electromagnetic scattering from small metallic nanoparticles, with a focus on integral equation and quasi-analytic approximation approaches. The T-matrix method is developed for solving the vector wave equation using integral equations. Finite-difference time-domain (FDTD) simulations are also performed and compared to T-matrix results. An analytic approximation is derived in the quasi-static limit that separates the wavelength, size, and shape dependencies of the internal field. This approximation agrees well with numerical solutions and provides physical insight into plasmon resonances of spheroidal and cylindrical nanoparticles.