The ability to adapt to the demands of a rapidly changing world is currently considered as a competence that is critical for engineering students to successfully self-actualize in the professional field. Therefore, the significance of the coordinated efforts of universities and stakeholders aimed at ensuring the flexibility of the teaching and learning is immensely increasing. Such efforts are the part of the effective formation of the future engineers’ ability to adapt to changing circumstances and environments as well as the ability to engage in lifelong learning. The goal of this work is twofold. At first, this study focuses on the challenges and opportunities for modern engineering and engineering education in the Industry 4.0 framework. The key requirement to future engineers’ skills and competences, that had been caused by intensive development of Industry 4.0, are reviewed. It was shown that flexibility and adaptability are considered by accreditation boards, researchers, and teachers as mandatory skills for modern engineers. Also, the concept of flexible teaching and learning is reviewed. The structure of flexible teaching and learning is analyzed in order to outline the directions and ways of its introducing in an engineering curriculum. The organizational and pedagogical framework for ensuring the flexible teaching and learning is proposed. Such framework is based on an analysis of modern requirements to future engineers. Also, the peculiarities of the system of Ukrainian engineering education had been taken into account. The proposed organizational and pedagogical framework includes five interconnected aspects, that are related to issues of the institutional support of educational process, the evolution of the content of an engineering education in the framework of Industry 4.0, the pedagogical approaches that are should be used, ways of using of information and communication technologies in an engineering education, and the personal values and motivation of students. It is emphasized that the institutional support plays an important role in improving the flexibility of the educational process by supporting the integration into the educational process of innovative student-centered approaches to teaching and learning. The increasing role of information and communication technologies leads to the necessity to introducing blended learning approaches as obligatory element of engineering degree programmes.