When a plasma is confined by magnetic fields inside a cylindrical conducting wall, the configuration of equilibrium can have either circular symmetry or helical symmetry. Thus, a sharp‐boundary screw pinch can have a circular or helical interface between the plasma and the vacuum. Each possesses the same amounts of total plasma mass, axial magnetic flux in plasma, axial magnetic flux in vacuum, and total azimuthal magnetic flux. It is shown that in the neighborhood of a point of bifurcation there are stable long‐wavelength helical equilibria. The equivalent circular equilibria with the same plasma mass and magnetic fluxes are unstable.