The stability of the Fadeev-like current sheet with respect to transversally propagating kink-like perturbations (flapping mode) is considered in terms of two-dimensional linear magnetohydrodynamic numerical simulations. It is found that the current sheet is stable when the total pressure minimum is located in the sheet center and unstable when the maximum value is reached there. It is shown that an unstable spot of any size enforces the whole sheet to be unstable, though the increment of instability decreases with the reduction of the unstable domain. In unstable sheets, the dispersion curve of instability shows a good match with the double-gradient (DG) model prediction. Here, the typical growth rate (short-wavelength limit) is close to the DG estimate averaged over the unstable region. In stable configurations, the typical frequency matches the maximum DG estimate. The dispersion curve of oscillations demonstrates a local maximum at wavelength similar to 0.7 sheet half-width, which is a new feature that is absent in simplified analytical solutions. (C) 2018 Author(s).