Design exploration is an important step in the engineering design process. This involves the search for design/s that meet the specified design criteria and accomplishes the predefined objective/s. In recent years, machine learning-based approaches have been widely used in engineering design problems. This paper showcases Artificial Neural Network (ANN) architecture applied to an engineering design problem to explore and identify improved design solutions. The case problem of this study is the design of flexible disc elements used in disc couplings. We are required to improve the design of the disc elements by lowering the mass and stress without lowering the torque transmission and misalignment capability. To accomplish this objective, we employ ANN coupled with genetic algorithm in the design exploration step to identify designs that meet the specified criteria (torque and misalignment) while having minimum mass and stress. The results are comparable to the optimized results obtained from the traditional response surface method. This can have huge advantage when we are evaluating conceptual designs against multiple conflicting requirements.