Abstract: The process of producing ethylene oxide through ethylene oxidation is simulated by a operation-type steady flowsheeting technique with a simultaneous-modular approach. Based on Upadhye and Grens rule, a practical method of selecting some tear streams in the same tear group is presented. By choosing properly as tear ones some streams whose corresponding functional relationship is known, the number of dimensions of a system of nonlinear equations is sharply reduced; thus the computation time and storage requirement are decreased apparently. In accordance with the characteristic strong non-linearity of chemical processes, we present the algorithm in which the discrete Newton method and QuasiNewton method are used alternatively as the one-dimensional incomplete searching method to solve the system of non-linear equations. Meanwhile a new method of calculating initial step size in one-dimensional searching is suggested. The system simulation shows that the algorithm works well and the calculated results agree with the measured data.