Exact Riemann wave solutions to the magnetohydrodynamic equations for a compressible medium under the influence of a gravitational field are obtained. The method of solution consists of an application of Hamburger's subsidiary equations previously found useful in the analysis of such three‐dimensional waves in compressible hydrodynamics under gravity. The resultant magnetoacoustic waves cannot be classified as slow and fast modes, and their propagation characteristics are found to be quite different from those in a uniform medium. In particular, the phenomenon of large amplitude wave ducting is examined. Certain wave properties correspond exceedingly well with the observed fine structure of waves propagating away from solar flares.