A significant growth in the volume of high-rise construction gives special relevance and urgency to the problem of safety of such facilities. Scientifically grounded plans of people’s evacuation, including all sorts of scenarios for people’s evacuation from buildings are developed for such structures. Scenarios include simulations of the motion of human flows along corridors, stairs, using elevators and mobile evacuation vehicles. An unresolved part of the problem is the problem of the rational choice and accommodation of people in stationary and mobile evacuation vehicles. The MIP model of the rational choice and accommodation of people in mobile vehicles of evacuation from buildings was developed. A particular case of the model – optimization of accommodation of people in the emergency evacuation vehicles according to the sequence of people’s arrival from the flow – was explored. The basic features of the model were analyzed: the model of the problem of mixed integer programming with piecewise continuous objective function. The specific features of the model allowed reasonable boiling down the problem to a sequence of sub-problems of accommodation the first objects (people) according to the sequence of their arrival and adapt each of them to the solution employing the multistart method with the application of artificial basis. A three-component model is considered as objects (of human bodies). The model is subject to restrictions that ensure the conditions for "gluing" the model's components into a single complex object. Continuous rotations of the model components with limitations to the turning angles are allowed. The proposed models and the solution methods modified in the present research make it possible to find both the configurations of the optimal-local accommodation of complex objects and the spatial shapes of objects.