A simple one-dimensional Cartesian solution of the magnetohydrodynamic equations describing the global motion of interstellar matter including the effects of cosmic-ray and magnetic-field pressure is presented. First an adiabatic equation of state for the thermal background plasma and a loss-free cosmic-ray gas in the strong-scattering limit is considered. In this case only one type of flow is consistent with the physical constraints: a subsonic wind at the base which accelerates for all values of galactic height (z) but never becomes supersonic. Second, a nonadiabatic interstellar gas is discussed. Including additional heating causes an acceleration to higher velocities. The presented solutions can be used to model halo components of interstellar matter with large-scale heights.