In this work the authors investigate a random field model describing the constitutive behavior of laminated composites. They model the material as a random hyperelastic medium which is characterized by a spatially dependent, stochastic and anisotropic strain energy function. The strain energy function is parametrized by a set of material parameters which are modeled as non-Gaussian random fields. Furthermore, they address the issue of identification of the parameters defining the random fields. This is performed by a two-step method, where in the first step, the mean model is calibrated by imposing a match between the linearized model and nominal values proposed in the literature. In the second step, parameters controlling the fluctuations are estimated by solving an inverse problem in which principal component analysis and the maximum likelihood method are combined. The whole framework is illustrated using an experimental database where multi-axial measurements are performed on a carbon-epoxy laminate.