Strong shock wave (SW) can be generated during underwater electrical wire explosion as the exploding wire rapidly expands and pushes the surrounding water. In this paper, a coupled model that describes the behaviours of the circuit, the exploding wire, and the evolution of SW was established. Wide range equation of state (EOS) data and conductivity data were used, making the calculation from solid state possible. The calculated discharge current, voltage across the wire, and trajectories of the wire radius and SW front were generally in good agreement with the experimental results, manifesting the validity of the model. Evolution of SW peak pressure, the process of energy conversion, and the effect of the discharge period were studied using the model. Simulation results showed that the radial attenuation of SW peak pressure is largely dependent on wire diameter and energy deposition process, while the efficiency of converting the deposited electrical energy to the mechanical energy of SW is not as sensitive, varying from 40% to 50% tens of microsecond after the current starts. Fast discharge tends to generate SW with higher initial SW peak pressure, while slow discharge enables higher initial energy storage within the limit of insulation and generates SW with slower radial attenuation. The presented model and numerical results could serve as a reference for parameter selection in related applications.