In this paper, an approximate method for determining the unstable regions of dynamic stability of thin-walled beams is given. The beam is assumed to be under the actions of concentrated longitudinal forces at both ends and of the type where P_0 =const., P_1(t) a periodic force with period 2π/(ω) and μ a small parameter. The end conditions are arbitrary. By using trigonometric series or Galerkin's method satisfying the end conditions, the fundamental equations, based on Vlasof's theory, are reduced to a system of three ordinary linear differential equations (4) or (7) of 2~(nd) order with periodic coefficients. Moreover, they can easily be transformed to canonical form Therefore, their characteristic equations are reciprocal equations, with characteristic roots symmetrically distributed with respect to the real axis and unit circle in a complex plane. The condition of boundary lines between stable and unstable regions is taken as, that all of the characteristic roots have unit modulus (absolute value), but there exist equal roots. Expanding the characteristic exponentials in series of the small parameter μ, this condition is represented by the following equations: where ω_(ni)ω_(nk) represent different frequencies of n-mode vibrations of the beam under the action of a constant force P_0, and ω is the frequency of P_1(t). When UUUU-0, (27) and (28) become Hence, dynamic unstability would take place at the neighbourhoods of these critical ratios, expressed by (29) and (30). When the unstable regions of dynamic stability are desired, we use perturbation method to determine a_(nj)~(i). For practical use, it is sufficient to determine a_(nj)~(1), a_(nj)~(2) only. The boundary lines can then be approximately determined by the following equations: For illustrating this method, a simply supported beam of narrow rectangular cross-section, under the action of varying end moments (fig. 2) is considered. The fundamental unstable regions, corresponding to bending, torsional and mixed type of dynamic unstability are calculated and shown in figs. 4, 3, 5.