<p>This article introduces two matrix-variate asymmetric distributions for modeling data exhibiting skewness and latent scale variability: the matrix-variate shifted asymmetric Laplace (MVSAL) and the matrix-variate shifted generalized asymmetric Laplace (MVSGAL). Both distributions arise within the class of matrix-variate normal mean-variance mixtures, yielding a hierarchical representation that facilitates random generation and likelihood-based inference. Several structural properties are established, including closure under linear transformations and marginalization. An Expectation/Conditional Maximization (ECM) algorithm is developed for maximum likelihood estimation, and simulation results demonstrate accurate parameter recovery with improved stability as the sample size increases. An empirical application to seasonal climatic data from 100 municipalities in the state of São Paulo illustrates the practical use of the MVSGAL model in a multivariate matrix setting, capturing temporal persistence, cross-variable dependence, and asymmetric effects within a unified framework.</p>