Waviness defects in composite laminates are known for potentially having a significant influence on the mechanical performance, especially on the longitudinal compressive strength; but they have mainly been studied in thermosetting matrix components. The objective of this study is to investigate both experimentally and numerically the effects on the elastic properties, damage scenarii, and failure stresses of out-of-plane waviness defects in laminates made of unidirectional plies of carbon fibres with a thermoplastic matrix. In a first step, 0°-90° cross-ply specimens with and without out-of-plane waviness are manufactured. The defects are artificially generated by introducing excess lengths with over-sized plies in a framed mould prior to consolidation. In order to relate the effects of the defects to their geometrical characteristics, a parametric model of the waviness shape is proposed and the parameters are identified from micrographs and tomography images before performing the mechanical tests. The effect of the generated out-of-plane waviness defects is studied experimentally with quasi-static layup under in-plane compression loading. During the test, machine load history and displacement data are collected. The strain fields on the surface of the specimens are obtained by digital image correlation. The damage scenario is captured on the specimen edge during the test by an additional camera zoomed in on the defect. For the numerical simulations of the effects of the defects, a model representative of each specimen is created from non-destructive data obtained before the tests. The mesh of the defect is generated by moving the nodes of a regular mesh so that the interfaces describe the shape of the identified waviness. Finally, the ONERA Progressive Failure Model is used to model the mechanical behaviour at the ply scale, accounting for the elastic non-linearity in the fibre direction, viscoelasticity, and both inter-fibre and fibre damage. Delaminations between the plies are modelled by cohesive zone models. The numerical simulations qualitatively capture the effects of defects and are consistent with the experimental results. They revealed a local reduction of the elastic properties at the location of the maximum fibre deviation and a reduction of the failure strength depending on the severity of the defect. The experimentally observed damage scenario is qualitatively well captured by the model.