<p>This manuscript addresses the problem of testing the multivariate skew normal distribution hypothesis when parameters are unknown. Data transformations to observations with approximately univariate normal distribution are employed to propose four computationally efficient tests for this composite hypothesis. The Shapiro-Wilk test is applied for assessing the normality of the transformed data. Existing normal approximations are used for computing the critical constants of this test, avoiding the use of expensive resampling techniques like parametric bootstrap. The size and power properties of these procedures are studied by means of Monte Carlo simulation, including different parameter configurations under the null and alternative hypotheses. Two of the proposed procedures have pretty good control of the type I error probability under the considered settings. Real data examples are included to illustrate the utility of the tests.</p>