This paper proposes a new method for studying the single valley characteristic of the cylindricity objective function which is seldom studied up to now. It is very important to computing its extreme value correctly by optimization principle to make sure that a cylindricity objective function is a single valley one or not. By means of a computer, we can rapidly determine whether any cylindricity objective function is a single valley one or not by the method proposed in the paper. Therefore, the problem which is very difficult to solve by pure mathematical method is solved.