Human resource (HR) risks are significant negative aspects of any organization. The main problem in the theory and practice of modern organizations is that there is no complex model and algorithm for managing HR risks. To define the essence of HR risks and basic approaches to their management, the authors conducted a survey of employees concerning the HR sphere. The authors used cluster and correlation–regression analysis to process the results of the survey conducted among employees about HR risks. Relying on general scientific research methods, data from open sources, including the review of scientific papers of foreign and national researchers and practitioners, and considering the opinions of the sociological survey respondents, the authors concluded that there is a need for carrying out close work with personnel to prevent conflicts in the working environment, increase the motivation for work, and involve the management team in regulating labor relationships. The scientific novelty of the study is that it considers the process of managing HR risks from a systemic perspective, while they are monitored based on the conceptual model suggested in the study. The models developed by the authors can be used in reality for managing HR risks faced by economic entities.