Real world data often fail to meet the underlying assumptions of normal statistical theory. Many statistical procedures in the psychological and educational sciences involve models that may include a system of statistical equations with non-normal correlated variables (e.g., factor analysis, structural equation modeling, or other complex applications of the general linear model). Monte Carlo techniques were used to test the appropriateness of statistical procedures when the underlying assumptions of these procedures are violated. There is a paucity of methods for generating systems of statistical equations in a simple and efficient manner. Thus, the focus of the current study was to derive a general procedure for simulating correlated non-normal systems of statistical equations with a focus on computational efficiency. The procedure allows for the systematic control of correlated non-normal: (1) stochastic disturbance terms; (2) independent variables; and (3) dependent and independent variables within a system. A numerical example is provided to demonstrate the procedure. The results of a Monte Carlo simulation are provided to demonstrate that the proposed method generates the desired population parameters and intercorrelations. Two appendixes illustrate the derived method. (Contains 1 figure, 3 tables, and 42 references.) (Author/SLD)