We study the effect of the stochastic character of supernova explosions on the anisotropy of galactic cosmic rays below the knee. We conclude that if the bulk of cosmic rays are produced in supernova explosions the observed small and nearly energy independent amplitude of the anisotropy and its phase are to the large extent determined by the history of these explosions in the vicinity of the solar system, namely by the location and the age of the supernova remnants, within a few kpc, which give the highest contribution to the total intensity at the present epoch. Among the most important factors which result in the small magnitude and the energy independence of the anisotropy amplitude are the mixed primary mass composition, the effect of the single source and the galactic Halo. Special attention is given to the phase of the anisotropy. It is shown that the excessive cosmic ray flux from the outer Galaxy can be due to the location of the solar system at the inner edge of the Orion arm which has the enhanced density and rate of supernova explosions.