The paper considers the transformation of human resource management processes in the healthcare settings of Ukraine in the context of war and the COVID-19 pandemic. It is noted that the unstable and hostile environment of a healthcare setting during times of crisis leads to the need to change the personnel selection and team formation model to increase the adaptability and resilience of human resources involved in the provision of medical care. The key features of the human resource management process in a turbulent environment are the high migration activity of personnel, which leads to the need to reallocate resources, the need to operate under severe financial constraints, and the need to consider personnel as a non-renewable resource when it is impossible to attract additional resources. To ensure the reliability of the functioning of a medical institution, the transformation of human resource management processes should be based on strategic agility and human resource management, organizational resilience as a resource-based capability, corporate sustainability, and transformation of enterprises’ resources, which can be achieved by applying methodological support for resource management in a multi-project environment. Considering a network of medical institutions as a multi-project environment will allow using the methodology of project-oriented resource management, forming adaptive teams in a multi-project environment, to ensure flexible redistribution of resources both within a single institution and within a network of institutions. It is proposed to use formal transformations to manage a medical institution’s human resources. Applying the proposed approach for managing the human resources of a medical institution is considered. The formation of a project team that satisfies the minimum requirements with the maximum value of the team’s qualification score is considered. It is shown that the use of this methodological support made it possible to choose the composition of the project team with a minimum number and a maximum value of the characteristic.