A dynamic modeling of an axially narrow-band oscillating cantilever beam was presented.The motion equations for the axially oscillating cantilever beam were derived by using the Kane's equation combining with Rayleigh-Ritz method.The method of multiple scales was used to solve directly the nonlinear differential equations and to derive the nonlinear modulation equation for the principal parametric resonance.The largest Lyapunov exponent was numerically obtained to determine the almost sure stability or instability of the trivial response of the system,and the validity of the stability was verified by direct numerical integration of the equantion.