The role of the dawn-dusk magnetic field component in stabilizing of the magnetotail flapping oscillations is investigated in the double-gradient model framework (Erkaev et al., Phys. Rev. Lett. 99, 235003 (2007)), extended for the magnetotail-like configurations with non-zero guide field By. Contribution of the guide field is examined both analytically and by means of linearized 2-dimensional (2D) and non-linear 3-dimensional (3D) MHD modeling. All three approaches demonstrate the same properties of the instability: stabilization of current sheet oscillations for short wavelength modes, appearing of the typical (fastest growing) wavelength lambda(peak) of the order of the current sheet width, decrease of the peak growth rate with increasing B-y value, and total decay of the mode for B-y similar to 0: 5 in the lobe magnetic field units. Analytical solution and 2D numerical simulations claim also the shift of lambda(peak) toward the longer wavelengths with increasing guide field. This result is barely visible in 3D simulations. It may be accounted for the specific background magnetic configuration, the pattern of tail-like equilibrium provided by approximated solution of the conventional Grad-Shafranov equation. The configuration demonstrates drastically changing radius of curvature of magnetic field lines, R-c. This, in turn, favors the "double-gradient" mode (lambda > R-c) in one part of the sheet and classical "ballooning" instability (lambda < R-c) in another part, which may result in generation of a "combined" unstable mode. (C) 2015 AIP Publishing LLC.