[en] The effect of different outer conducting configurations on the stability of a cylindrical plasma of radius a is treated with emphasis on the k approx. 0, n = 1 mode associated with the usual surface perturbation e/sup ikz+-in theta. The conducting configuration comprises of either one or more segments of a cylindrical shell or conducting cylinder with gaps in it, or segments lying in the radial plane. The stability effects of the various geometries are compared through their resulting value for the minimum vacuum energy integral. An asymptotic technique is developed for fins of infinite extent. For a/c sufficiently small, fins in the radial planes theta = 0, π and +-π/2 at a distance c from the axis, tend to have the same stabilization effect on the n = 1 mode as a concentric outer cylinder of radius B where B = √2c. For more general geometry including fins of finite extent, the problem is then formulated in terms of a singular differential-integral equation which is then reduced to a regular Fredholm integral equation which can be solved numerically. Results are given for a circular segment (-α < theta < α, r = A) for various values of the half-angle α and radius A, both in the presence of and absence of a complete circular outer conductor