To increase the use of polymeric structural composites, a major issue is to properly account for intra-laminar failure mechanisms, such as fiber kinking which is typically induced in compression. We propose a new set of continuum damage models that are able to predict fiber kinking response under compression. A structure tensor based formulation is established at the unidirectional ply level, where the elastic material response is governed by transverse isotropy. To consider geometrical effects in conjunction with fiber kinking instability, a continuum damage formulation at finite strain is developed. The fracture area progression includes a convective and a local damage production involving a finite progression speed. In this framework, two damage evolution models are considered; one non–local model including the gradient damage effect and a local one, without the gradient enhancement. The models are implemented in a FE–code and validated for a compression loaded specimen. The models are computationally robust and can predict the localized nature of fiber kinking. A thorough sensitivity study is presented to show how the different formulations influence the predicted responses.