This paper addresses the issues of modeling of individual workspaces of a human and a collaborative robot, as well as their intersections, taking into account the requirements of the safety of their interaction without losses in the efficiency of collaboration. Methods of safe human-robot collaboration have been considered. A review of a human functioning in a workspace within both the easy-to-access, and the optimum area depending on his motor functions has been undertaken. The approaches to solving the problem of human movement using a discrete cellular automata method, and the problem of intersection of the working bodies of a robot and a human have been considered. A model in the MATLAB simulation environment has been formed, which allows to create clouds of points of workspaces for both a robot and a human, taking into account the anthropometric parameters of a human, the dimensional characteristics of a collaborative robot, and their relative locations. In addition, the initial stage of numerical modelling has been carried out in order to form a separate cloud of points of intersection of the working areas of a collaborative robot and a human worker, as well as to calculate its approximate volume.