The exact analytical solutions of the Schrodinger equation for the generalized symmetrical Woods-Saxon potential are examined for the scattering, bound, and quasi-bound states in one dimension. The reflection and transmission coefficients are analytically obtained. Then, the correlations between the potential parameters and the reflection-transmission coefficients are investigated, and a transmission resonance condition is derived. Occurrence of the transmission resonance has been shown when incident energy of the particle is equal to one of the resonance energies of the quasi-bound states. (C) 2016 AIP Publishing LLC.