Galaxies with highly active star formation regions (starburst galaxies) are inferred to have high supernova rates in the region of activity1,2. If most of the supernova energy input is thermalized, a strong wind is driven out of the active region. The wind is probably so fast that gravitational forces are not involved. We present here an analytical solution for the wind which is driven from a region of uniform mass and energy deposition. The solution is applied to M82-the best observed case of a starbust galaxy. The model can be directly compared with the gas pressure in M82 and with a wind velocity deduced from radio spectra. The galaxy does have clouds orbiting out of the disk. The interaction of the wind with the clouds can give rise to streaming motions and to X-ray emission. The wind is expected to create a hole in any diffuse gas in which the galaxy is embedded. The wind may have a significant role in the evolution of a starburst galaxy in that it transfers gas, which is probably heavy-element enriched, from the central regions to the outer parts of the galaxy.