With the development of the design and manufacture technology, composite materials are widely used in the aeronautical industry. But, one of the main concerns which affects the application of composites is foreign object impact. The damages induced by the Low Velocity Impact (LVI), which can significantly reduce the strength of the structures, can’t be easily inspected routinely. The so-called Barely Visible Impact Damages (BVID) due to LVI typically includes interlaminar delamination, matrix cracks and fibre fracture at the back face. Previous researches have shown that the results of LVI test are similar to that of the Quasi-Static Load (QSL) test. The initiation and propagation of delamination can be detected more easily in the QSL test and the displacement and reaction force of the impactor can be controlled and measured much more accurately. Moreover, it is easier to model QSL tests than dynamic impacts. To investigate the impact damage induced by LVI, a Finite Element (FE) model employing cohesive elements was used. At the same time, the ply clustering effect, when several plies of the same orientation were stack together, was modelled in the FE model in terms of damage resistance and damage size. A bilinear traction-separation law was introduced in the cohesive elements employed to simulate the initiation and propagation of the impact damage and delamination. Firstly, a 2D FE model of the Double Cantilever Beam (DCB) and End Notched Flexure (ENF) specimens were built using the commercial FEM software ABAQUS. The results have shown that the cohesive elements can be used to simulate mode I and mode II delamination sufficiently and correctly. Secondly, an FE model of a composite plate under QSL but without simulating damage was built using the continuum shell elements. Agreement between the FEA results with published test results is good enough to validate the capability of continuum shell elements and cohesive elements in modelling the composite laminate under the transverse load condition (QSL). Thirdly, an FE model containing discrete interface delamination and matrix cracks at the back face of the composite plate was built by pre-setting the cohesive failure elements at potential damage locations according to the experimental observation. A cross-ply laminate was modelled first where fewer interfaces could be delaminated. Good agreement was found in terms of the delamination area and impactor’s displacement-force curve. Finally, the effect of ply clustering on impact damage resistance was studied using Quasi-Isotropic (QI) layup laminates. Because of the limited time available for calculation, the simulation was only partly completed for the quasi-isotropic laminates (L2 configuration) which have more delaminated interfaces. The results showed that cohesive elements obeying the bilinear traction-separation law were capable of predicting the reaction force in quasi-isotropic laminates. However, discrepancies with the test results in terms of delamination area were observed for quasi-isotropic laminates. These discrepancies are mainly attributed to the simplification of matrix cracks simulation and compressive load at the interface in the thickness direction which is not taken into account.