© 2016 Elsevier B.V.This paper presents the modelling of tensile failure of composites using novel enriched elements defined based on the floating node method. An enriched ply element is developed, such that a matrix crack can be modelled explicitly within its domain. An enriched cohesive element is developed to incorporate the boundaries of matrix cracks on the interface, such that the local stress concentrations on the interface can be captured. The edge status variable approach allows the automatic propagation of a large number of matrix cracks in the mesh. A laminate element is formed, such that a fixed, planar mesh can be used for laminates of arbitrary layups. The application examples demonstrate that the proposed method is capable of predicting several challenging scenarios of composites tensile failure, such as the large number matrix cracks, grip-to-grip longitudinal splits, widespread delamination, explosive splitting and distributed fibre breaking in the 0 plies, etc. The complete failure process of ply-blocked composite laminates, up to the final breaking of the loosened 0° strips, is here firstly reproduced by modelling