The present work is focused on the computational challenges and further verification and validation of an advanced fibre kinking model. This model was previously developed by the authors and implemented in a Finite Element (FE) code with a mesh objective formulation. The previous validation in terms of comparison with an analytical and micromechanical model is herein extended to also encompass FE simulations in longitudinal compression and multiaxial stress states. In addition, numerical improvements have been added to the model targeting its computational efficiency and stability in order to handle multiaxial stress states and large structures.