Two-step hybrid asymptotic method based on perturbation methods and phase integrals (method WKB) is used to obtain approximate analytical solutions of the nonlinear problem of the vibrations of the aircraft near the rough surface, which reduces the need for the integration of singular nonlinear differential equation with time-variable periodic coefficients for given initial conditions. This solution is not limited to the value of the dimensionless amplitude of perturbations and the nature of the order non-linear restoring force. The resulting solution has the form of the sum, where each term consists of two functions according to the method of perturbation (in scalar parameter when the nonlinear component of the original equation) and the WKB-approximation, effective in the integration of singular differential equations with variable coefficients. For specific numerical results, a comparison with the data of direct numerical integration of the equations of the original problem.

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