Uncertainty quantification of composite materials is more challenging than for traditional quasi-homogeneous engineering materials due to a number of physical and mechanical parameters as well as the interaction of two or more components. Traditional probabilistic methods based upon statistical moments analysis bring a lot of information, whose common usage and analysis may be difficult, especially when different probability distributions are analyzed at the same time; the same concerns homogenized characteristics of various composites. Therefore, some alternative approach is proposed, where instead of Bayesian probability calculations Shannon entropy and probabilistic distance are engaged to carry out such uncertainty analysis for the fibrous and particulate composites. The uncertainty sources are material and physical characteristics of the components as well as the geometrical properties of the interphases. The homogenization method is based on the Finite Element Method (FEM) calculation of the deformation energy of the Representative Volume Element of both materials. Probabilistic analysis is based upon a specifically designed series of FEM experiments as well as dual recovery of the response functions – using both the Weighted Least Squares Method as well as the artificial neural network (ANN) approach. The response functions including input uncertainty sources are further employed in the Monte-Carlo simulations, stochastic generalized perturbation technique as well as the semi-analytical method for the calculation of Shannon and Bhattacharyya entropies. Such an analysis answers how input uncertainty affects the resulting statistical scattering of the homogenized properties of these composites and also enables us to determine the probabilistic sensitivity of these properties. Numerical studies are developed using the commercial FEM system ABAQUS, the academic software MCCEFF developed by the Author as well as the computer algebra system MAPLE 2024. An example of the application of this methodology in experimental-based studies of modern composites will also be shown.