The formulation of a solution method for the equilibrium stage model equations involves six major decisions. Each of these decisions is analyzed and the proper choices indicated. One major contribution of the analysis was a clearer understanding of why any one solution method is not convergent on both distillation and absorber types of problems. A correct solution method is formulated for absorption and extraction problems. This method when programed in parallel with a distillation method works all but a few unusual problems with a minimum of computer time. Another contribution was the development of a procedure for solving the concentration or component rate matrix equations which avoids the computational difficulties of the Lewis-Matheson and Thiele-Geddes methods; that is the procedure avoids truncation error build up, does not require mesh points, works equally well for any number of feeds and side streams, and handles nondistributed components in the same way as distributed ones.