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This theoretical study, deals with the effect of bi-particle interaction on the surface plasmon resonance (SPR) in a dimer which includes two identical metal nanoparticles (NPs). Considering the dipole-dipole interaction in a Drude-like model, an appropriate equation is derived for the permittivity of each NP. The restoration force related to the classical confinement originating from the finite size of NPs is considered and an appropriate adjustment coefficient is considered for this term through analyzing experimental data. Two different polarizations are considered for the laser beam electric field and it is shown that the orientation of electric field has essential role in the linear optical properties of dimer. Numerical investigation is accomplished for a dimer of gold NPs with two different diameters of 4nm and 20nm. For the parallel polarization, dipole-dipole interaction leads to the red-shift of SPR wavelength and increase in its peak value while for the perpendicular polarization, the absolutely opposite results are derived. For all cases, it is shown that SPR wavelength functionality with respect to the geometric factor $a/d$ (NP radius to the separation) can be presented by a cubic equation that fits better than an exponential one suggested by the earlier studies which demonstrates the dipole-dipole characteristic of the interaction. Qualitatively, our results are in good agreement with the other experimental studies.