Disclosed are systems and methods for modeling behavior of game elements during a remote game between at least two users. The system includes a positioning module configured to determine parameters for at least two game elements representing physical objects, and game manipulators that detect a physical action performed by a user in order to exert a force action on at least one game element and calculate one or more physical parameters characterizing the physical action. The system further includes a module for performing force actions that determines the game element to be subject to the detected physical action and perform a force action on the determined game element. The system further includes a control module that determines behavior parameters for the game elements characterizing a change in state of the game elements, and a visualization module that generates a behavior model of the game elements.