We calculate the equilibrium position of a plasma column of round cross section inside an ideally conducting housing for the case when the axis of the plasma column (or the housing) represents a space curve. For calculation we use the model of a plasma column with a sharp boundary and a surface current. Solution is presented in the form of a Fourier-series expansion over the are length of the column axis. For the case when the curvature is a smooth function of the are length, simple formulas have been obtained for displacement of the column axis with respect to the axis of the housing, the validity of which, for the case when the housing has the shape of a racetrack, is confirmed by numerical calculation of the displacement by general formulas. Use of the same method of Fourier-series expansion enables one to solve even the problem of the distortion of the plasma column caused by transverse slits in the housing that are necessary for the introduction of the electric field into the discharge volume where plasma is created. Calculation results are given of distortions by slits in a toroidal housing.