A KDF 9 computer and a micro-film recorder have been used to generate and plot out random crater distributions, and to make 16-mm film of the developing patterns. These studies have shown: (1) that continuing generation of random craters with an inverse square law size distribution produces a mean crater density equal to that observed on the Moon, together with local variations analogous to the Lunar Highlands and Mare. (2) that overlapping and obliteration do not change the size distribution exponent of the remaining craters significantly from –2, although the exponent relating to craters with unbroken rims is affected, (3) that the virtual absence on the Moon of smaller craters overlapped by larger ones arises because of their burial under the outer slopes of the larger crater walls; (4) that crater counts on fixed areas do lead to systematic error, caused by exclusion of large craters from the sample. Further simulations might include the effects of erosion, flooding, and secondary cratering mechanisms, and might also be used for statistical studies.