Summary: Consider an experiment in which \(m\) measurements are observed in each of \(n\) treatments (for example, different dosages of a drug). When the experimenter is interested in the differences of the treatment effects, statistical testing of the corresponding mean vectors for skew populations necessitates a new model, which is called the matrix variate of skew normal distributions. We propose the model and derive the moment generating function and distribution of the quadratic forms of such random matrices. We show that the quadratic form of a skew normal matrix variate follows a Wishart distribution.