Equilibrium models are constructed of a cool, dense, interstellar gas cloud, surrounded by a hot, tenuous H II region, and permeated by the locally distorted galactic magnetic field. The cloud is assumed to be axisymmetric, isothermal with a temperature of 75 K and to be of mass I0 M0. The detailed solutions show that the cloud is oblate about its axis of symmetry and becomes highly flattened as the strength of the background magnetic field is increased. In an equatorial region the field exerts considerable pinching forces and in some models the field lines have snapped off, forming neutral rings. The effects of uniform rotation about the axis of symmetry of the magnetic field are examined.