Experimental investigation of machining is cost prohibitive. The number of parameters to control, the exhaustive material characterisation and the time consuming procedure to determine the mechanical responses like cutting forces restricts experimental studies. In this context, mathematical modelling can be a feasible tool for studying the various responses in machining. This paper presents an attempt to investigate orthogonal machining of unidirectional Glass Fibre Reinforced Plastic Composite (UD-GFRP) materials using mathematical modelling. The model entailing fibre orientation, shear strength, depth of cut, feed, friction angle and rake angle is constructed for investigating the tangential cutting and feed cutting force developed during machining. The numerical results are compared to the experimental results. The comparison indicates that the model provides satisfactory prediction of the cutting forces. The relations between process parameters are discussed.