The estimation of several missing values in a randomized block design ls considered. The method used ls that of minimizing the error sum of squares, proposed originally by Yates (1933). Explicit equation for each absent value are derived for all cases in which not more than three values are missing. A general formula valid for any permissible number of missing observations ls given for the case in which no two values are missing in the same block or treatment, and also for the case in which all of the values missing are in a single block or treatment. A procedure for the completely general case is proposed. This, although requiring the inversion of s symmetric matrix of order equal to the number of missing observations, may prove to be less tedious in application than the iterative method proposed by Yates.