  The prospect of stabilization of the $m=1$ ``rigid'' ballooning mode in an
open axially symmetric long-thin trap with the help of a conducting lateral
wall surrounding a column of isotropic plasma is studied. It is found that for
effective wall stabilization, the beta parameter must exceed $70\%$. The
dependence of the critical beta on the mirror ratio, the radial pressure
profile, and the axial profile of the vacuum magnet has been studied. It is
shown that when a conductive lateral wall is combined with conductive end
plates simulating attachment of the end MHD stabilizers to the central cell of
an open trap, there are two critical beta values and two stability zones that
can merge, making stable the entire range of allowable beta values $0<\beta<1$.
