This paper presents a novel approach to micromechanical modelling of plain woven polymer matrix composites and predicting the overall response including the nonlinear and rate-dependent behaviour. The nonlinearity and rate-dependence of plain woven composites is evaluated by describing the behaviour of the polyer matrix using a viscoplastic model. The damage evolution of the yarn material and deformation of the woven fabric are investigated by considering Weibull distribution based formulations and a shear-modulus discount approach, respectively. The explicit meshfree method with time-dependent periodic boundary conditions for unit cell (UC) models that describe the internal architecture of plain woven composites is presented for the first time. For validation, numerical examples are performed to simulate the EP121-C15-53 plain woven composite subjected to in-plane normal/off-axis tensile loading conditions and at three different strain rates, i.e. 10−1 s−1, 10−3 s−1 and 10−5 s−1. Good agrements are found between the numerical and experimental results, with both the quasi-linear, rate-insensitive behaviour in the normal direction and the nonlinear, rate-dependent response in the off-axis direction successfully predicted.