Carbon fibre reinforced plastic (CFRP) composites are found to be cut satisfactorily by a pulsed Nd:YAG laser at the optimum process parameter ranges. Predictive models have been developed based on important process parameters, viz. cutting speed, pulse energy, pulse duration, pulse repetition rate and gas pressure. The responses considered are the heat-affected zone (HAZ) and the taper of the cut surface. The optimisation of process parameters was done using response surface methodology (RSM). The thermal properties of the constituent material and the volume fraction of the fibres are the principal factors that control the cutting performance. The effect of the process parameters on the output responses is also discussed.