In this paper, the stability analysis of the elastic columns subjected to seven different types of the nonconservative force is investigated on the basis of fully intrinsic beam equations. The generalized differential quadrature method is used for the discretization of the first-order intrinsic equations and corresponding boundary conditions. Altogether, four important boundary conditions—simply supported, clamped-simply supported, clamped-free, and clamped-clamped conditions—are considered. Furthermore, the effect of the combined action of an end-concentrated force and a distributed tangential follower force is investigated. To confirm the validity of the proposed intrinsic formulations, the present results are compared with those obtained from classical formulations. Our results reveal that the fully intrinsic formulation is a suitable framework to model nonconservative problems.