Abstract: Observations that are made on p response variables and each response variable is measured over n sites or time points, construct matrix-variate response variable, and arise across a wide range of disciplines, including medical, environmental and agricultural studies. The observations in an (n x p)-dimensional matrix-variate sample are not independent, but are doubly correlated. The popularity of the classical general linear model (CGLM) is mostly due to the ease of modeling and authentication of the appropriateness of the model. However, CGLM is not appropriate for doubly correlated matrix-variate data. We propose an extension of CGLM for matrix-variate data with exchangeably distributed errors for multiple observations. Maximum likelihood estimates of the matrix parameters of the intercept, slope and the eigenblocks of the exchangeable error matrix are derived. The distributions of these estimators are also derived. The practical implications of the methodological aspects of the proposed extended model for matrix-variate data are demonstrated using two medical datasets.