The article presents the development of a mathematical model, which lets forecast the characteristics of evacuation processes in aviation transport systems. The developed model is based on the system dynamics approach. The model is created with usage of cause-effect links among characteristics and is presented by a system of nonlinear differential equations. Numerical methods were used for getting a solution of the system of nonlinear differential equations. The computational experiments carried out based on the developed model for determination the characteristics of the passengers’ evacuation process from airplane’s side effects at different time intervals. The developed mathematical model was verified by comparing the results of computational experiments with testing evacuations’ data. The models and results obtained in the paper can be used in designing next-generation aviation systems.