The box selectivity in operational stack of container terminal is a quite common and long studied question. The purely random sample is governed by the theory of probability offering some combinatorial estimations. It is pointed that the introduction of operational rules like import/export separation, storage along shipping lines, sorting by rail or truck transportation etc., as well as the most notorious «immersion» effect, that is, covering of boxes arrived earlier by next cargo parties, blurs the clear algebraic picture and leads to appearance of many heuristiс approaches to solving the problem. It is figured out in the paper that a new impetus to this problem in last decades was given by the rapid development of IT, AI and simulation techniques. The scientific publications describing many models of real and abstractive terminals, into which complex mechanisms that reflect specific features and selected strategies are built, are considered in the paper. Unfortunately, these models are usually created ad hoc, with some pragmatic objectives and under the demand of closest possible proximity to the simulated objects. It is proved that there are much less models designated to purely scientific study of the deep inner mechanisms responsible for the primal behavior of the operating container stack, enabling to introduce the new rules and restrictions step by step, providing regular proving every next stage adequacy and ease to use. The research boils down to formulating the specific container handling equipment technology in container selection operations and detecting the dependencies between number of moves necessary to select a container and the geometric features of a stack.