Plasmonic excitations in a three interacting nanocylinder cluster have been investigated by both simple analytical modeling and discrete dipole approximation (DDA) calculations. In our analytical model, each cylinder is regarded as an anisotropic electric dipole with four parameters determined by fitting its optical extinction and scattering spectra to that of DDA simulation. Diagonalization of our analytical model for the three interacting dipoles reveals 10 significant plasmon modes, namely, 5 bright modes and 5 dark eigen-modes. Because of rather long-range longitudinal plasmon coupling, the resonant energies of the two longitudinal modes vary pronouncedly with the intercylinder distance even when the intercylinder distance is about 25 times larger than the cylinder diameter. In contrast, for the transverse modes the splitting of resonant energies becomes apparent when the intercylinder distance falls within about five times of the cylinder diameter. Interestingly, for sufficiently large clusters, each resonance peak contains both magnetic dipole (M1) and electric quadrupole (E2) as well as electric dipole (E1) contributions, and these multipole contributions become rather visible (“bright”) when the distance between the two neighboring cylinders is sufficiently reduced. Finally, the optical plasmon excitation spectra from our simple analytical model are in good qualitative agreement with our DDA calculations.