In engineering design and analysis, proper assessment of stochastic features of model outputs is essential to account for the existence of various uncertainties. Monte Carlo simulation provides a viable tool to reproduce the stochastic features of the model outputs by generating statistically plausible realizations for random model inputs and parameters. Although there are a variety of generators developed for problems involving univariate random variable or independent random variables, generating multivariate random variates is more restricted to a few distributions whose joint probability density functions (PDFs) are known. Since most engineering problems involve multiple correlated random variables whose joint PDF is normally very difficult to establish, practical algorithms are needed to generate correlated random variables with a mixture of marginal distributions and correlation structure or even less information. In this paper, the third-order polynomial normal transform (TPNT) technique is applied to the Monte Carlo simulation, which enables one to generate correlated random variables with much less information than joint PDF. Using the TPNT, arbitrary univariate or multivariate random variates can be generated from univariate or multivariate normal distributions utilizing orthogonal transform and normal transform. The information needed is the marginal distributions and correlation structure, or sample data of the involved random variables. As compared with the existing model, the proposed algorithm shows comparable results with less information required.