This article examines eight measures of skewness and the Mardia measure of kurtosis for skew-elliptical distributions. Multivariate measures of skewness considered include Mardia, Malkovich-Afifi, Isogai, Song, Balakrishnan-Brito-Quiroz, Móri-Rohatgi-Székely, Kollo, and Srivastava measures. We first study the canonical form of skew-elliptical distributions and then derive exact expressions of all measures of skewness and kurtosis for the family of skew-elliptical distributions, except for Song’s measure. Specifically, the formulas of these measures for skew normal, skew t, skew logistic, skew Laplace, skew Pearson type II, and skew Pearson type VII distributions are obtained. Next, as in Malkovich and Afifi (1973), test statistics based on a random sample are constructed for illustrating the usefulness of the established results. In a simulation study, different measures of skewness and kurtosis for 2-dimensional skewed distributions are calculated and compared. Finally, real data is analyzed to demonstrate all the results.