Abstract: Multivariate t distributions belong to elliptically contoured distributions. However, they are symmetric. In many fields such as economics, psychology and sociology, sometimes error structures in a regression type models no longer satisfy symmetric property. Generally there is a presence of high skewness. Therefore, multivariate skew elliptical distributions have been developed. In this paper, properties about known family of multivariate skew t distributions are stressed. Linear transformations, marginal and conditional density are given. Also moments are derived.