Fibre kinking is one of the main failure modes of composite laminates under compression loading. In thispaper, the role of kinking in the failure of quasi-isotropic composites subjected to a bearing load is investigated. High-resolution CT scans show that kinking is largely involved in the events leading to laminate collapse, notably by triggering other damage modes such as delamination. Kink bands develop extremely progressively, leading to the formation of a wide localization zone (or FPZ, failure process zone). Such behaviour calls for a non-local modelling approach. Local damage models would lead to overly conservative sizing. A simple model, based on Hashin failure criteria and non-local effective stresses is confronted to experiments, and its limits are highlighted. It will be shown that proper modelling of the bearing failure requires the characteristic behaviour of kink bands to be taken into account.