The population’s access to quality medical services is one of the indicators that reflects the country’s level of development from a social perspective. The quality of life of citizens largely depends on their health status. No matter how wealthy a person may be, if they are ill, they cannot fully enjoy life. The rate of population aging in EU countries is high; with age, chronic diseases emerge, and the need for medical care increases. Therefore, the object of study, “unmet need for medical examination and care,” remains relevant. The main objective of the study is to verify the hypothesis that the number of practicing doctors, dentists, and hospital beds influences the “unmet need for medical examination and care.” By applying software EViews 9.5, the type of correlation between the endogenous variable “unmet need for medical examination and care” and the exogenous variables—the number of practicing doctors, dentists, and hospital beds—was established. Regression analysis was conducted to achieve the proposed goal. The indicator “unmet need for medical examination and care” suggests that dissatisfaction with medical services has increased in every second member state of the European Union over the past five years. However, in other EU countries, the number of satisfied individuals with the availability and quality of health services is increasing. In most EU countries, except for four, the number of hospital beds per hundred thousand inhabitants and hospitals has decreased in the last twelve years. Despite the surge in diseases during the COVID-19 pandemic, the downward trend persists. Thus, in some EU countries, there is a consistent downward trend in patient satisfaction with the accessibility and quality of medical care. The results obtained in this study support the hypothesis that the number of practicing doctors, dentists, and hospital beds influences the “unmet need for medical examination and care.” It was also found that, compared to other countries, in the case of France, the regression coefficient between the number of doctors and the “unmet need for medical examination and care” is the largest (in absolute value).