Surface plasmon resonances of two-dimensional silver nanoparticles under the electrical dipole source and TE wave are investigated. By using Maxwell’s equations and multi-multipole method, a set of linear equations of expansion coefficients is first constructed by satisfying boundary conditions pointwisely. Singular value decomposition is then used to solve the overdetermined linear equations. The far field responses are estimated by calculating the scattering cross section. An electromagnetic field radiated by a two-dimensional electric dipole source in the infinite domain is first derived. Then, an analytical series expansion solution of the scattering between an electrical dipole and a cylinder is presented. Numerical results of single, solid/core-shell and two solid cylindrical nanoparticles under the electrical dipole source with resonance frequency are presented. It is demonstrated from numerical results that the resonances wavelength of core-shell nanoparticles strongly depends on the shell thickness. It is also observed that different positions and orientations of the electric dipole source do not change the resonance peak of a single metal nanocylinder. In order to solve the half-plane problem, a scattering base function which satisfies boundary conditions of the interface is derived. Incident field of TE wave or electrical dipole source is modified to satisfy the boundary conditions of the interface. Numerical results of varied nanoparticles lie on the dielectric substrate under the electromagnetic source are presented. Compare with infinite domain problem, the dielectric substrate changes the surface plasmon mode and the enhanced electromagnetic field on the nanoparticles.