MHD stabilization of flute and ballooning modes in an axisymmetric mirror trap is studied under the assumption of strong finite Larmor radius effect that suppresses all perturbations with azimuthal numbers and makes the m = 1 mode 'rigid'. The rigid mode can be effectively suppressed using perfectly conducting lateral wall without any additional means of stabilization or in combination with end MHD anchors. Numerical calculations were carried out for an anisotropic plasma produced in the course of neutral beam injection into the minimum of the magnetic field at the right angle to the trap axis. The stabilizing effect of the conducting shell made of a straightened cylinder is compared with a proportional chamber, which, on an enlarged scale, repeats the shape of the plasma column. It is confirmed that for convincing wall stabilization of the rigid modes, the plasma beta (β, the ratio of the plasma pressure to the magnetic field pressure) must exceed some critical value . When conducting lateral wall is combined with conducting end plates imitating MHD end anchors, there are two critical betas and, respectively, two stability zones and that can merge, making the entire range of betas allowable for stable plasma confinement. The dependence of the critical betas on the plasma anisotropy, mirror ratio, width of the vacuum gap between the plasma column and the lateral wall, radial pressure profile and the axial magnetic field profile is examined.