This paper presents a general method for generating asymmetric multivariate densities by perturbing symmetric distributions, with a focus on the multivariate skew t distribution. The approach is applicable to various symmetric distributions, including the skew normal distribution. The paper examines the properties of skew elliptical densities, which are symmetric distributions modified by a skewing factor. It also introduces a multivariate skew t distribution, which is a generalization of the multivariate t distribution, allowing for asymmetry in the data. The paper discusses the likelihood inference for this distribution and provides numerical examples. The skew t distribution is shown to be a flexible tool for modeling data with skewness and heavy tails. The paper also explores the connections between different forms of skew elliptical distributions and their properties, including their behavior under transformations and conditioning. The skew t distribution is derived as a special case of the more general skew elliptical family, and its properties are analyzed in detail. The paper concludes with a discussion of the implications of these results for statistical modeling and inference.This paper presents a general method for generating asymmetric multivariate densities by perturbing symmetric distributions, with a focus on the multivariate skew t distribution. The approach is applicable to various symmetric distributions, including the skew normal distribution. The paper examines the properties of skew elliptical densities, which are symmetric distributions modified by a skewing factor. It also introduces a multivariate skew t distribution, which is a generalization of the multivariate t distribution, allowing for asymmetry in the data. The paper discusses the likelihood inference for this distribution and provides numerical examples. The skew t distribution is shown to be a flexible tool for modeling data with skewness and heavy tails. The paper also explores the connections between different forms of skew elliptical distributions and their properties, including their behavior under transformations and conditioning. The skew t distribution is derived as a special case of the more general skew elliptical family, and its properties are analyzed in detail. The paper concludes with a discussion of the implications of these results for statistical modeling and inference.