A semi-analytic method is proposed for the generation of realizations of a multivariate process of a given linear correlation structure and marginal distribution. This is an extension of a similar method for univariate processes, transforming the autocorrelation of the non-Gaussian process to that of a Gaussian process based on a piece-wise linear marginal transform from non-Gaussian to Gaussian marginal. The extension to multivariate processes involves the derivation of the autocorrelation matrix from the marginal transforms, which determines the generating vector autoregressive process. The effectiveness of the approach is demonstrated on systems designed under different scenarios of autocovariance and marginals.