This paper deals with the problem of determining the optimal shape of the board trajectory and the evaluation of the stability factor, in order to ensure the stability of the boards, increasing the safety of overburden mining in the process of open-cut mining. In determining the trajectory of the boarder the method of cubic splines is used. To apply this method, the length of the base of the quarry (or ledge) is divided into arbitrary n parts and in each partial segment is constructed corresponding cubic spline function, being combined, each curve in common, gives a general curve corresponding to the profile of the trajectory of the pit wall.