Ultrasonic techniques providing fast and non-destructive method are reliable for elastic behavior and damage characterization of polymer-matrix composite materials. In this paper, an approach focused on ultrasonic immersion measurements is proposed to extract the effective stiffness tensors for composites having different level of anisotropic mechanical behavior. The approach relies upon the ultrasonic velocities measured in symmetrical and non-principal propagation planes which are combined to constrained optimization algorithms to solve iteratively the Christoffel's equation. It must be emphasized that the present work does not consider Lamb waves and focuses exclusively on transmitted ultrasonic bulk waves. First, the theoretical framework is concisely reviewed. Next, the mixed experimental-numerical ultrasonic approach is then detailed and the representation of stiffness curves is proposed. The developed approach has been experimentally validated through several examples of undamaged and damaged materials. The damage was initiated by drop-weight low velocity impact and its accumulation has been investigated after a tension-tension fatigue test. Three types of polymer matrix composites were studied: (i) Rovicore (R) glass fiber/Polyester processed by RTM, (ii) Unidirectional glass E/phenolic and (iii) Randomly oriented glass fiber/Polyester. Good agreements have been obtained by comparing the overall stiffness tensor from ultrasound measurements with the experimental data achieved by destructive mechanical testing. Stiffness reductions induced by impact and fatigue post impact damage was clearly identified for whole tensor components. The results proved the capability of developed approach to estimate the stiffness reduction and to highlight the inherent damage induced anisotropy.