Stability properties are investigated for purely growing (Re&ohgr; = 0) tearing modes at marginal stability (Im&ohgr; = 0) for a rotating, nonrelativistic cylindrically symmetric ion layer immersed in an axial magnetic field. The analysis is carried out within the framework of a Vlasov‐fluid model in which the electrons are described as a macroscopic cold fluid, and the layer ions are described by the Vlasov equation. Tearing‐mode stability properties are calculated numerically for azimuthally symmetric perturbations about an ion layer equilibrium with temperature anisotropy. The marginal stability eigenvalue equation is solved numerically for the perturbation amplitude and the normalized axial wavenumbers at marginal stability in terms of temperature anisotropy, layer radius, and magnetic field depression on the axis. It is found that the range of unstable wavenumbers decreases as T‖‖/T⊥is increased, and numerical estimates are made of the anisotropy required for complete stabilization.