This graduate project work focuses on the practical application of Josephson tunneling. Using the time-dependent Schrödinger equation, we derived the mathematical expressions for current density (J), phase difference , magnetic flux ) and frequency oscillation ( ). Using the derived equations, we plotted and discussed the phase diagrams of current versus voltage, current density versus voltage, magnetic flux versus phase difference, and current density versus magnetic flux. The results obtained are in broad agreement with the experimental findings. For further or extensive studies on Josephson tunneling, this project would be used as a base line.