In social and behavioral sciences, data are typically not normally distributed, which can invalidate hypothesis testing and lead to unreliable results when being analyzed by methods developed for normal data. The existing methods of generating multivariate non-normal data typically create data according to specific univariate marginal measures such as the univariate skewness and kurtosis, but not multivariate measures such as Mardia's skewness and kurtosis. In this study, we propose a new method of generating multivariate non-normal data with given multivariate skewness and kurtosis. Our approach allows researchers to better control their simulation designs in evaluating the influence of multivariate non-normality. [This paper was published in "Behavior Research Methods" v52 p939-946 2020.]