Conditions for the instability and the fragmentation of expanding and decelerating shells are discussed. A self-similar analytical solution is compared with the results of 3-dimensional computer simulations of expansions in homogeneous media. The amount of energy supply from the final number of young stars in an OB association, the value of the sound speed, the stratification and density of the ambient medium, the galactic differential rotation and the gravitational force perpendicular to the galactic plane influence formation of fragments. The typical size of unstable shells is 1 kpc for density n = 1\ cm(-3) . In thick disk galaxies the fragmentation occurs in the nearly whole shell while in thin disks it is restricted to the galactic equator. Unstable fragments may become molecular and trigger the formation of molecular clouds where new stars are formed. We conclude that in dwarf galaxies the star formation may propagate in all directions turning the system into a starburst, contrary to spiral galaxies where the star formation propagates only in some directions in the thin strip near the symmetry plane.