This paper presents some theoretical aspects and a set of experiments concerning the climbing of a straight staircase by a hexapod robot. For the theoretical foundation, a suitable strategy was first defined, later included in two algorithms. For the experimental part, a simulator created in the Matlab environment was built and used, which allowed the graphic visualization of the representative steps associated with the proposed strategy for climbing this type of obstacle. Also, a simplified physical model of the hexapod robot, equipped with its own driving system, was also built. Its ultimate utility is to allow comparisons between the results of graphical simulations and real physical behaviors to adopt possible corrections. At the end of the paper, several images captured with this physical model during the experiment carried out according to the proposed strategy are included.