The presence of defects in composite materials is hardly avoidable during the process of materials manufacturing, which may affect the mechanical behaviour of the material. This paper presents a Representative Volume Element (RVE) based Discrete Element model (DEM) for analysing the effects of defects on the transverse mechanical response of unidirectional (UD) fibre-reinforced polymer (FRP) laminae. Using the DEM model, crack initiation and propagation in defective RVEs with different fibre distributions are analysed and compared. In addition, the effects of the distribution of the defects on stress–strain responses are also investigated. The DEM model shows excellent capabilities in predicting the crack path at failure that is consistent with experimental tests. Based on a data set generated by 1000 DEM simulations, back-propagation deep neural network (DNN) models are developed for a fast determination of crack initiation and instantaneous critical load of the RVEs. The results show that both the initial crack and the critical stress of the laminae can be accurately and efficiently predicted by the data-driven DNN models with consideration of randomly distributed defects.