For some classes of materials, the size of the Representative Volume Element (RVE) can be much larger than the one of the domain typically used in experimental testing or structural applications. This work is dedicated to the construction, experimental identification and use of a probabilistic model for the random elasticity tensor of such media at mesoscale. For this purpose, two kinds of approaches are considered. The first one relies on the combination of a probabilistic model for the mesoscopic volume fraction and a mean-field homogenization technique. As a very first application, the methodology is applied to a longfiber reinforced composite whose experimental characterization is performed by using an ultrasound analysis. The results allow the experimental trajectories of the random field to be identified by solving an inverse problem. The identification of the of the probabilistic model parameters is carried out by using the Maximum Likelihood Principle. The second approach is based a probabilistic model for the elasticity tensor random field that was recently proposed in the literature.