A survey of ring galaxies which were discovered in 1960 by B. Vorontsov-Velyaminov has been carried out using the Morphological Catalogue of Galaxies. Clusters of galaxies were also included. Such galaxies without spiral arms constitute 0.7% of all galaxies down to 15m.0, and are 100 times less frequent than spiral galaxies. This percentage is the same for clusters, but there are fields where ring galaxies are 3–5 times more frequent than the average. the probability of nearly central chance collisions of galaxies as proposed by some theories has been calculated. It was assumed that a ring galaxy is formed from the encounter of a spiral galaxy with another galaxy if its mass or luminosity is not less than 1% of that of the principal galaxy. the minimum separation of their centres was taken to be less than 2.7 kpc, but the angles between the vectors of the relative velocity and the planes of galaxies were not restricted. the lifetime of the rings once they are formed was assumed to be 109 years and the distribution of the galactic velocities was calculated according to a Maxwellian distribution. the number of galaxies of given absolute magnitude per unit volume was taken from Holmberg (Stars and Stellar Systems, 9, 123). the curvature of the trajectories was taken into account. So conditions were chosen to be most favourable for nearly central collisions.