A micromechanical approach was utilized to predict damage mechanisms in glass fibre/polypropylene (GF/PP) thermoplastic composites. First, we systematically determine a representative volume element (RVE) of such materials using a two-point probability function and the eigenvalue stabilization of homogenized elastic tensor. Next, the 3D finite element models of the RVE were developed accordingly. We implemented a set of constitutive models capable of describing the behaviour of GF/PP under various loading conditions with the focus on pressure- and rate-dependent behaviours of polypropylene. The RVE was then imposed with periodical boundary conditions and subjected to transverse tensile loading accordance with experimental tensile tests on 8 laminates. The simulation results were in excellent agreement with experiments including the nonlinearity and the failure point, making it a useful virtual testing tool for composite material design. The effects of the main parameters that can be tailored in such materials were then investigated to provide guidelines for future improvements of the materials. It was found that increasing matrix ductility is not an effective strategy to improve the strength and ductility of the composite while increasing the inter-fibre distance could significantly delay the initiation of a transverse crack.