Abstarct: There are many practical situations for which a symmetric model doas not fit well to the give data set, and the plot of data is skew. Thus an skew model can be fitted better. Forther if there exist extreme values and outliers in the data heavier tail alternatives to the skew normal models, such as Students-t skew distribution or more generally scale mixture of skew normal distributions perform better for model fitting purpose. In this thesis multivariate skew normal distributions with one and two skewness parameters are studied in details and as an extension to the letter, a new multivariate scale mixture of skew normal distributions model is defined, and its statistical properties are obtainded.