A study is made of the structure and properties of material balance simulation problems, and a technique is developed for their efficient solution. The method requires neither simultaneous solution of all balance equations nor iterative convergence methods. Instead, for each stream mixing point in the flow sheet, a vector balance equation is developed which contains as unknowns only mixer output streams. This unique set of vector equations is sequenced for solution by using precedence ordering and substitution techniques. It is shown that only as many vector equations need to be solved simultaneously as there are streams which would require iteration in the conventional sequential approach. Once the mixer output streams are calculated, the remaining intermediate process streams are evaluated directly with no further equation solving. Computational results are presented showing the efficiency of the method.