  The stabilization of ``rigid'' flute and ballooning modes $m = 1$ in an
axisymmetric mirror trap with the help of an ideally conducting lateral both in
the presence and in the absence of end MHD anchors is studied. The calculations
were performed for an anisotropic plasma in a model that simulates the pressure
distribution during the injection of beams of fast neutral atoms into the
magnetic field minimum at a right angle to the trap axis. It was assumed that
the lateral wall has the shape of a cylinder with a variable radius, so that on
an enlarged scale it repeats the shape of the plasma column.
  It has been found that for the effective stabilization of the listed modes by
an ideally conducting lateral wall, the parameter beta ($\beta$, the ratio of
the plasma pressure to the magnetic field pressure) must exceed some critical
value $\beta_{\text{crit}}$. When combined with a conducting lateral wall and
conducting end plates imitating MHD end stabilizers, there are two critical
beta values and two stability zones $0<\beta<\beta_{\text{ crit}1}$ and
$\beta_{\text {crit}2}<\beta<1$ that can merge, making the entire range of
allowable beta values $0<\beta<1$ stable.
  The dependence of the critical betas on the degree of plasma anisotropy, the
mirror ratio, and the width of the vacuum gap between the plasma and the
lateral wall is studied. In contrast to the works of other authors devoted to
the plasma model with a sharp boundary, we calculated the boundaries of the
stability zone for a number of diffuse radial pressure profiles and several
axial magnetic field profiles.
