In view of nuclear structure calculations, the second Pöschl–Teller potential is parameterized to study nucleon–nucleon and nucleon–nucleus elastic scattering. By exploiting the variable phase approach to potential scattering, phase parameters, cross sections, analyzing powers, etc., are computed and compared with earlier works. The calculated cross sections agree with the experiments below 25 MeV within the error bars for the (n-p) and (n-d) systems.