One of the most important issues in engineering is the monitoring and the early detection of structural damages to prevent catastrophic failures. This process is referred to as Structural Health Monitoring and is expected to provide considerable improvements with respect to safety and maintenance costs. More particularly, the focus is here put on composite structure representative of aeronautic applications and the damages to be monitored are of “delamination” type. Nonlinear features generated by Lamb wave/damage interaction were employed for the detection of the delamination damage. Experiments are conducted on composite plates made of carbon fiber reinforced polymer equipped with two piezoelectric transducers. One plate is calibrated with a delamination damage at the center using laser shock wave technique. Nonlinear features of Lamb waves are observed in the experimental results. Finite element method is here used for investigating the nonlinear wave properties as well as the wave/damage interaction. Two damage models are studied and implemented at delamination area: a spring model and a contact model. An undamaged plate is also presented as reference in both finite element simulations and experiments. Results show that higher harmonics can be used as identification of the existence of delamination damage in a composite structure. A contact interaction model can represent the mechanical behavior of delamination damage and can be used for a real delamination modelling.