We have derived the free energy landscape for the translocation of a single vesicle through a narrow pore by accounting for bending and stretching of the vesicle, and the deformation of the vesicle by the pore. Emergence of a free energy barrier for translocation is a general result, and the magnitude of the barrier is calculated in terms of the various material parameters. The extent of the reduction in the barrier by the presence of an external constant force is calculated. Using the Fokker-Planck formalism, we have calculated the average translocation time corresponding to the various free energy landscapes representing different parameter sets. The dependencies of the average translocation time on the strength of the external force, vesicle size, bending and stretching moduli of the vesicle, and radius and length of the pore are derived, and the computed results are discussed.