The rapid advancement of Generative Artificial Intelligence (GAI) has created new opportunities and challenges for engineering education, particularly in Mechanical Engineering Education (MEE). This study investigates the adoption and use of GAI in MEE. Drawing on a literature review and semi-structured interviews with faculty members and students, key enablers, challenges, strategies, and psychological factors influencing GAI adoption were identified. Survey data were subsequently analysed using the Relative Importance Index (RII) to prioritize the factors perceived as most influential by both stakeholder groups. The findings indicate that strategy-related factors, particularly institutional governance and clear policies for GAI use, were prioritized by both faculty members and students. Pedagogical and ethical considerations were perceived as more influential than technical barriers. Furthermore, students perceived GAI to be most valuable for technically intensive tasks, including design, simulation, and coding, whereas collaborative applications received the lowest priority. Overall, the findings provide evidence-based insights into the factors influencing GAI adoption and the areas in which students perceive the greatest value for its application, supporting the structured and pedagogically aligned integration of GAI within Mechanical Engineering Education.