The nonlinear dynamic equations for axially compressed anisotropic thi
n-walled beams are discretized by means of Fourier expansion and Galer
kin procedure obtaining a set of nonlinear ordinary differential equat
ions. Based on these ordinary differential equations the buckling and
initial post-buckling behavior is analysed. The formulas for initial p
ost-buckling slope and curvature are derived. In the case where the co
mpressed force is a harmonic function of time, the frequency range and
amplitudes of the parametric resonance (instability) are calculated.