Using electrodynamics theory, we numerically demonstrated that when the incident light polarization direction is parallel to a silver rod axis, the modes that are forbidden in a fully illuminated silver rod can be excited when the rod is partially illuminated. The modes are excited due to the symmetry breaking of the rod when it is partially illuminated. They are characterized by the even number of nodes in the excited surface plasmons and quadrupole pattern of the scattered light in the space. These modes are different from the allowed modes in a fully illuminated rod, which shows an odd number of nodes in the excited surface plasmons and a dipole pattern of the scattered light. The conclusion was further supported by the calculation results when the illuminated spot was moved from the rod end to its center and when the illuminated length was varied. We also demonstrated dark modes when the incident light polarization is perpendicular to the rod axis. Contrary to the hypothesis that a dark mode will be an efficient waveguide mode, the dark mode shows very poor waveguide applications when the incident polarization is perpendicular to the rod axis.