We use a linearized model of kinetic MHD for the perturbative calculation of growth rates of Alfven eigenmodes.The numerical model, a code called CAS3D‐K, is based on the three‐dimensional ideal MHD stability code CAS3D and a numeric solution of the drift kinetic equation which avoids approximations to the magnetic geometry but neglects the drifts of the particles away from the flux surface.The approach is used to discuss stability boundaries in W7‐X and W7‐AS and considers both, passing and reflected particles. The limits of the applicability of the model will be discussed as well.It will be shown that gyro‐kinetic PIC codes offer a very promising way to improve the model. The two‐dimensional linear PIC code GYGLES is used to calculate gyro‐kinetic counterparts of ideal MHD modes in cylindrical and in tokamak geometry.