Fibre-reinforced plastics (FRPs) are used in structural components in various fields of application of mechanical engineering, such as automobile, biomechanics and aerospace industries. Their own properties, particularly the high strength and stiffness and simultaneously low weight, allows the substitution of the metallic materials in many cases. As a result of these properties and potential applications, exist a great necessity to investigate the machining of these composite materials. This paper presents an optimisation study of surface roughness in turning FRPs tubes manufacturing by filament winding and hand lay-up, using polycrystalline diamond cutting tools. A plan of experiments was performed with cutting parameters prefixed in the FRP tubes. The objective was establishing the optimal cutting parameters to obtain a certain surface roughness (R-a and R-t/R-max), corresponding to international dimensional precision (ISO) IT7 and IT8 in the FRP workpieces, using multiple analysis regression (MRA). Additionally, the optimal material removal rates have been obtained.