In this paper, the linear buckling of Cross Laminated Timber walls is investigated. A 3D numerical study using finite-elements is presented for several Cross Laminated Timber geometries, ply configurations and boundary conditions. First, it is shown that critical buckling loads are close to the material failure load which proves the necessity of a design model for the buckling of Cross Laminated Timber panels. Second, through a comparison between soft simple support boundary conditions and conventional hard simple support conditions, it is shown that this distinction could be taken into account for designing timber structures depending on the accuracy needed. Third, several plate models, particularly the Bending-Gradient theory, are compared to these 3D reference results. It is observed that for varying plate geometries and arrangements, the Bending-Gradient theory predicts more precisely the critical load of CLT panels than classical lamination and first-order shear deformation theories. Finally, it is demonstrated that one of the suggested projections of the Bending-Gradient on a Reissner-Mindlin model gives very accurate results and could favorably allow the development of engineering recommendations to estimate properly transverse shear effects.