Calculations and measurements of the Mueller matrix of an ellipsoidal mirror have been performed. In the calculations we have considered six different input polarization states to obtain a system of 24 equations, of which only 16 are independent, to yield 16 expressions for the elements of the Mueller matrix. We have compared experimental measurements of the elements of the matrix with the theoretical results. Some differences between theory and experiment have been found. Thess differences suggest that Mueller matrix ellipsometry could be used as an optical testing method.