Magnetohydrodynamic stability of force‐free spheromak plasmas ton= 1 free boundary tilt and radial shift modes is studied. The exterior region of open field lines is treated either as a conducting plasma or as a vacuum. In the former case the effect of line tying of the open field lines is present and is found to improve stability greatly. The equilibria which have optimum stability properties to the tilt and shift modes have a length‐to‐diameter ratio of 0.6, and can be stable with conducting walls at a relatively large distance.