Axially symmetric toroidal plasma equilibria with spherical or near‐spherical plasma‐vacuum boundaries are examined when variations in the distribution function produce anisotropic pressures. A separable analytic solution is found when the pressure deviation from isotropy is small; the degree of anisotropy is used as an expansion parameter in the perturbation scheme. In general, the plasma‐vacuum boundaries deform slightly and spherical boundaries cannot be maintained by externally applied fields that remain finite at large distances. Whenp⊥>p‖, the plasma becomes a prolate spheroid and whenp‖<p⊥it becomes oblate.