Whereas in an isotropic temperature atmosphere both the hydrostatic equation and the momentum equation give the same conditions for hydrostatic equilibrium, in the anisotropic case the situation is ambiguous. It is found that for an anisotropic temperature the hydrostatic equilibrium conditions have to be deduced from the momentum equation. The condition for hydrostatic equilibrium is that both the parallel and the perpendicular temperatures, to the radial direction, decrease more rapidly than 1/r in the general case and that the perpendicular temperature decreases more rapidly than 1/r when the parallel temperature is constant. The momentum equation displays a transonic solution when at least one of the temperatures, parallel or perpendicular to the radial direction, decreases less rapidly than 1/r in the general case and when the perpendicular temperature decreases less rapidly than 1/r when the parallel temperature is constant. In an anisotropic atmosphere the parallel thermal velocity is the critical velocity. The properties of the transonic expansion in an isothermal and anisotropic atmosphere are studied. The initial velocity, the critical distance position, the terminal velocity, and the density profile are significantly different from the isotropic case. These properties are opposite with respect to the value of the anisotropy T /T > 1.0 and T /T < 1.0. In particular, for a perpendicular temperature larger than the parallel temperature the acceleration starts really at a significant distance from the base of the atmosphere, whereas the critical point is closer to the base of the atmosphere compared to the isotropic case. For an opposite anisotropy the transonic point moves far away from the base of the atmosphere, and the terminal velocity is significantly decreased for small temperature anisotropy. The mass loss rate is drastically affected for an anisotropy T /T > 2.0. The extension of this study to multimoment anisotropic models can be useful for the interpretation of particle simulation of rarefied stellar atmosphere expansion.