The Wilcoxon two-sample test carried out in randomized blocks is discussed and exemplified. Tables of critical values are given for 1-sided (2-sided) significance levels of 0.001 (0.002), 0.005 (0.01), 0.01 (0.02), 0.025 (0.05), 0.05 (0.10), and 0.10 (0.20) for 1 to 30 equal replicates of each of the two treatments in 1 to 12 blocks. The normal and other approximations are assessed. A short computer program is given which will approximate the probability associated with a grand rank sum for unequal as well as equal replicates in any number of blocks.