A new code, MISHKA-D (Drift MHD), has been developed as an extension of the ideal MHD code MISHKA-1 in order to investigate the finite gyroradius stabilizing effect of ion diamagnetic drift frequency, ω*i, on linear ideal MHD eigenmodes in tokamaks with shaped plasma cross-section. The MISHKA-D code gives a self-consistent computation of both stable and unstable eigenmodes with eigenvalues |γ| ≅ ω*i in plasmas with strong radial variation in the ion diamagnetic frequency. Test results of the MISHKA-D code show good agreement with the analytically obtained -spectrum and stability limits of the internal kink mode, n/m=1/1, used as a benchmark case. Finite-n ballooning and low-n kink (peeling) modes in the edge transport barrier just inside the separatrix are studied for H-mode plasma with the ω*i-effect included. The ion diamagnetic stabilization of the ballooning modes is found to be most effective for narrow edge pedestals. For low enough plasma density the - stabilization can lead to a second zone of ballooning stability, in which all the ballooning modes are stable for any value of the pressure gradient. For internal transport barriers typical of JET optimised shear discharges, the stabilizing influence of ion diamagnetic frequency on the n=1 global pressure driven disruptive mode is studied. A strong radial variation of ω*i is found to significantly decrease the stabilizing ω*i- effect on the n=1 mode, in comparison with the case of constant estimated at the foot of the internal transport barrier.