Thomson coil is a well-known actuator for fast operation and hence it is used in applications such as DC circuit breakers for rapid switching. To achieve the required stroke length in the specified opening time, it is desirable that the moving disc has as low weight as possible. But this leads to high stresses due to bending which affects the long-term performance of the mechanism. This is improved by providing a support plate to the disc which reduces the stresses in the Thomson coil disc. The support plate is designed by formulating a shape optimization problem with the objective of minimizing the induced bending stresses in the support plate while ensuring that the desired stroke length requirement at opening time is met. The Thomson coil and disc parameters are defined to maximize benefit in terms of flux density and hence achieve maximum force. Using the forces from this model, stroke length at opening time and von-Mises stress data is generated by varying design parameters of radius, height at center and outer edge of support plate. This data is then used to develop a data-driven model by using regression techniques. Optimization algorithm is then used to obtain the optimum values of design variables followed by sensitivity analysis. It is further verified that the optimized support plate reduces the stresses in the Thomson coil disc.