X‐ray collimators using grid patterns which are random offer several significant advantages over collimators using periodic grids. In particular, random array grid collimators (RAGC’s) eliminate the requirement that there be very closely spaced grids if a wide field of obscuration outside the central peak is desired. The RAGC should be less susceptible to systematic off‐axis leaks, and the RAGC has a better high energy response than a periodic grid collimator. The random array technique can also be used to produce converging or diverging collimators. A general theory is presented which predicts the angular response of a RAGC. It is shown that pure random arrays have two problems: there are strong wings in the response function and the patterns are not self‐supporting. Restrictions on the randomness of the pattern are suggested which eliminate these problems but at the price of putting an upper limit on the available throughput. However, even in the worst case, the upper limit for a two‐dimensional collimator is as high as 23%. In other cases, throughputs the order of 40% are possible with two‐dimensional collimators and of 50% with one‐dimensional collimators. These techniques can provide 10 arc second two‐dimensional collimators with a large collecting area. Suggestions are presented for easing the fabrication effort of the grids.