The paper considers a numerical method for determining the robot workspace shell. The developed method allows forming the workspace shell as an N-dimensional array through sequential discrete checking of the robot’s boundary positions. Each of the array elements can take three values, the first of which means that the element is not checked, the second—checked and belongs to the workspace, the third—checked and does not belong to the workspace. At the initial stage, the method involves searching for an element belonging to the boundary of the workspace. This element is the starting one for iterative checking of other boundary elements. An algorithm for determining the workspace shell is synthesized and software implemented taking into account the possibility of determining the shell in an N-dimensional space of any dimension. Procedures for filling the internal areas of the resulting workspace shell for subsequent processing are implemented. The method is tested on the Gough-Stewart platform. The simulation results are presented.