Nowadays, advanced materials such as composite materials, thermoplastics, fibre glass etc. are replacing other materials in many different industrial applications. This is due to the improvements achieved in their engineering properties. The demand on these advanced engineering materials necessitates the development of advanced material processing techniques. Laser beam cutting (LBC) is an advanced processing technique applied widely in industry to cut different materials with high production rates. In order to optimise the LBC process, it is essential to first model the process accurately. In fact, an optimised cutting procedure is crucial to insure the high quality of the products. This procedure should contain the values, or ranges of values, for process parameters that produce cuts with the quality levels required by the end user. Accordingly, the aim of the current research is to apply response surface methodology (RSM) via Design-expert software to develop empirically based mathematical models that relate the process input parameters to the quality features (responses). Once these mathematical models have been developed and checked for their adequacy they can be used to optimise the process, and thus, achieve the desired quality levels. The LBC input parameters considered herein are: laser power, cutting speed, assist gas pressure, focal point position, nozzle diameter and stand-off distance. The quality features investigated are: upper kerf width, lower kerf width, ratio between two kerfs, heat affected zone (HAZ), roughness of the cut section and operating cost. Materials, commonly used in industry, in sheet form with different thicknesses, have been investigated namely: medical grade austenitic stainless steel AISI316L, medium density fibre board (MDF), Ultra-high molecular weight polyethylene (UHMWPE), polymethyl-methacrylate (PMMA) and glass fibre reinforced plastic (GFRP). A CW 1.5 kW CO2 Rofin laser is used to perform the cutting operations. Different models were successfully developed to predict the responses for each material and thickness including operating cost. Moreover, the main effects and interaction effects of the process parameters on the responses were determined, discussed and illustrated graphically. In addition, the process has been optimised and the optimal cutting conditions have been recorded for each material and thickness. These records could be used as a standard procedure for LBC because they provide the relevant parameters and allowable ranges that should be used for optimal laser cutting for each material and thickness.