SUMMARY A comparison is made of methods of generating samples on a computer from the Poisson distribution. The well-known methods of counting the number of occurrences in a Poisson process and of sequentially searching through a table of cumulative probabilities have the disadvantage that the time required increases with thePoisson parameter ft. For fixed ft two modified search procedures are described which remain fast as ft increases. If ft varies from sample to sample the modified search procedures are not directly applicable. But fast methods can be found which use combinations of either modified search method and are appreciably faster than rejection methods.