The whole set of the stiffnesses of materials that possess any class of symmetry, and then the higher symmetry coordinate system can be determined from wave speed measurements of obliquely incident ultrasonic bulk waves [1–2]. An immersion ultrasonic tank associated with a tensile machine allows one to measure the load-induced changes of the stiffness tensor [3]. The damage can be defined as the variation of the elasticity tensor [4]. No preliminary knowledge of the microstructure is required to describe the damage process. Concerning former works on off-axis loading [5], the choice of a tetragonal material submitted to a tensible solicitation at 45° from fiber directions , was imposed by the limiting hypothesis required by classical ultrasonic techniques that the material keeps its orthorhombic symmetry in a a priori known coordinate system.