We address the challenge of optimizing the interaction between medical personnel and treatment stations within mobile and flexible medical care units (MFMCUs) in conflict zones. For the analysis of such systems, a closed queuing model with a finite number of treatment stations has been developed, which accounts for the possibility of performing multiple tasks for a single medical service request. Under the assumption of Poisson event flows, a system of integro-differential equations for the probability densities of the introduced states has been compiled. To solve it, the method of discrete binomial transformations is employed in conjunction with production functions. Solutions were obtained in the form of finite expressions, enabling the transition from the probabilistic characteristics of the model to the main performance metrics of the MFMCU: the load factor of medical personnel, and the utilization rate of treatment stations. The results show the selection of the number of treatment stations in the medical care area and the calculation of the appropriate performance of medical personnel.