This paper discusses a possible approach to the solution of the problem of the stability of a thermonuclear plasma confined by a wall of finite, anisotropic and inhomogeneous conductivity. To simulate a spatially non-homogeneous structure (like, e.g., a cage of conducting rods), a model has been considered which assumes an anisotropic and space-dependent conductivity of the confining wall. It is shown that the effect of the region external to the plasma, including the conducting wall itself, can be taken into account simply by imposing a set of boundary constraints to the plasma variables at the plasma edge. These boundary conditions are derived for the most general case, while the linear stability of an RFP plasma surrounded by an anisotropic thin liner is discussed in order to understand the role of a resistive liner on the stability of the Padova RFX experiment.