Fibre reinforced plastics (FRP) contain two phases of materials with drastically distinguished mechanical and thermal properties, which brings in complicated interactions between the matrix and the reinforcement during machining. Surface quality and dimensional precision will greatly affect parts during their useful life especially in cases where the components will be in contact with other elements or materials during their useful life. Therefore, their study and characterisation is extremely important and, above all, those cases subjected to adverse environmental conditions and in contact with other elements or materials. Thus, measuring and characterising surface properties represent one of the most important aspects in manufacturing processes. In this paper, orthogonal cutting tests were carried out on unidirectional glassfibre reinforced plastics (GFRP), using cermet tools. During the tests, the depth of cut (a), feedrate (f), cutting speed (Vc) were varied, whereas the cutting direction was held parallel to the fibre orientation. Turning experiments were designed based on statistical three level full factorial experimental design technique. An artificial neural network (ANN) and response surface (RS) model were developed to predict surface roughness on the turned part surface. In the development of predictive models, cutting parameters of cutting speed, depth of cut and feed rate were considered as model variables. The required data for predictive models are obtained by conducting a series of turning test and measuring the surface roughness data. Good agreement is observed between the predictive models results and the experimental measurements. The ANN and RSM models for GFRPs turned part surfaces are compared with each other for accuracy and computational cost.