Fibre Bragg gratings (FBGs) fabricated in linearly birefringent fibres were embedded in glass fibre/epoxy composites and in the corresponding unreinforced resin to monitor the effective transverse strain development during the cure process. The optical fibres containing the FBG sensors were aligned either normal or parallel to the reinforcement fibres in unidirectional glass fibre/epoxy prepregs. The chemical cure kinetics of the epoxy resin system used were studied using differential scanning calorimetry, in order to investigate the correlation between the strain monitoring results and the evolution of the curing reaction. A non-parametric cure kinetics model was developed and validated for this purpose. The effective transverse strain measured by the FBGs demonstrated high sensitivity to the degree of cure as a result of the densification of the resin caused by the curing reaction. The effective compressive transverse strain developed during the reaction, and thus the corresponding sensitivity to chemical changes, was higher in the case of the sensing fibre aligned normal to the reinforcement fibres than in the case of the sensor fibre parallel to the reinforcement fibres. Small but measurable sensitivity to cure induced changes was observed in the case of the unreinforced resin.