The aim of this paper is to introduce a simplified model for an uncertain solid layer sandwiched between two acoustic fluid layers and using the ultrasonic characterization with an acoustic source placed in one fluid layer. Uncertainties are taken into account with a probabilistic model of the elasticity tensor. Its parameters are the mean value of the random tensor and a dispersion parameter that controls the statistical fluctuation level. The characterization of the solid layer given a database of actual measurements consists in the determination of the (i) elastic parameters of the mean elasticity model, (ii) the dispersion parameter, and (iii) mass density of the solid. This is performed with a numerical solver of wave propagation and for in vivo data collected previously. The model is representative of measurements of human bone properties with the so-called axial transmission technique. The capability of the model to predict the velocity of the first experimental arriving signal in the statistical sense is proved. The identified anisotropic elasticity tensor of cortical bone from actual data based on the simplified model is given.