Abstract <p>Modeling and clustering matrix variate data are crucial for solving real-time problems, as they provide robust tools for uncovering hidden structures and making data-driven decisions. This article introduces the finite mixtures of matrix variate skew-Laplace distributions to model and cluster skewed matrix variate data. To enhance the flexibility and applicability of the proposed framework, we introduce parsimonious mixture models by imposing constraints on the covariance matrices, thereby enabling the selection of appropriate models and facilitating analysis with smaller sample sizes. The parameters of the mixture models are derived and efficiently estimated using the Expectation Conditional Maximization (ECM) algorithm. Extensive simulation studies and real-world data applications demonstrate the effectiveness and robustness of the proposed methodology, highlighting its potential to uncover meaningful patterns in skewed matrix variate data.</p>