The aim of this work is to evaluate the effects of the heterogeneity and anisotropy of material properties of cortical bone on its ultrasonic response obtained by using axial transmission method. The heterogeneity and anisotropy of material properties are introduced by using a parametric probabilistic model. The geometrical configuration of the tested sample is described by a tri-layer medium composed of a heterogeneous and anisotropic solid layer sandwiched between two acoustic fluid layers of which one of these layers is excited by an acoustic linear source. The numerical results focus on studying of an interest quantity, called velocity of the first arriving signal, showing that it strongly depends on the dispersion induced by statistical fluctuations of stochastic elasticity field.