Identifying new problems and providing solutions are necessary tasks for design engineers at early-stage product design and development. A new problem fosters innovative and inventive solutions. Hence, it is expected that engineering design pedagogy and practice should equally focus on engineering design problem-exploring (EDPE)—a process of identifying or coming up with a new problem or need at the early-stage of design, and engineering design problem-solving (EDPS)—a process of developing engineering design solutions to a given problem. However, studies suggest that EDPE is scarcely practiced or given attention to in academia and industry, unlike EDPS. The aim of this paper is to investigate the EDPE process for any information relating to its scarce practice in academia and industry. This is to explore how emerging technologies could support the process. Natural models and phenomena that explain the EDPE process are investigated, including the “rational” and “garbage can” models, and associated challenges identified. A computational framework that mimics the natural EDPE process is presented. The framework is based on Markovian model and computational technologies, including machine learning. A case study is conducted with a sample size of 43 participants drawn worldwide from the engineering design community in academia and industry. The case study result shows that the first-of-its-kind computational EDPE framework presented in this paper supports both novice and experienced design engineers in EDPE.