Nonlinear effects on the stationary equilibrium of spheroidal low‐aspect‐ratio plasma shapes with vacuum boundaries are considered mainly using appropriate linear methods. Simple analyses of both magnetohydrodynamic and guiding center fluids with anisotropic pressuresp⊥andp∥nearly equal to the scalar pressurepare presented. Results concerning the necessary amount of axial currentI0required for equilibrium are given and their implications for stability are described.