The Knapsack problem (maximize a linear function, subject to a unique constraint, all being in integers), although of thenp-complete type, is a well solved case in combinatorial programming. The reason for this is twofold:(i)an upper bound of the objective function is easy to compute(ii)it is quite simple to construct feasible solutions. They give lower bounds of the optimum. This makes it possible to know rapidly the optimal value of many variables, and therefore to reduce the problem. Several studies have appeared recently on the subject [5, 9, 12, 18]. We present a program by which Knapsacks involving up to 60 000 boolean variables were solved in a matter of seconds, on an I.B.M. 370-168.