Although substantial work has been undertaken on reaction pathways involved in base-promoted elimination reactions and bimolecular nucleophilic substitution reaction of F- on CH3CH2X (X = Cl, Br, I), the effect of solvents with varying dielectric constants on the stereochemistry of each of the reaction species involved across the reaction profile have not yet been clearly understood. The present investigation reports the effect of solvents on the potential energy surfaces (PES) and structures of the species appearing in the reaction pathway of F- with bromoethane. The PESs in the gas phase have been computed at MP2 level and CCSD(T) level. The performance of several hybrid density functional, such as B3LYP, M06, M06L, BHandH, X3LYP, M05, M05-2X, and M06-2X have also been investigated toward describing the elimination and nucleophilic substitution reactions. With respect to MAE values and to make the computation cost-effective, we have explored the implicit continuum solvent model, CPCM in solvents like cyclohexane, methanol, acetonitrile, dimethyl sulfoxide and water. The reactant complexes proceed through the subsequent steps to produce fluoroethane as the substitution product and ethylene as one of the elimination products. For elimination reaction both syn and anti elimination have been explored. The calculated relatives energies values, which are negative in the gas phase, are found to be positive in polar solvents since the point charge in the separated reactants are more stabilized than the dispersed charge in the transient complex, which has also been analyzed through NBO analysis.