The aim of this work was to investigate the prediction of the elastic constants of carbon fibre-reinforced epoxy laminated composites using a simple mathematical approach. For this purpose, a Matlab Calculation Code (MCC) has been developed in MATLAB, which provides sufficient capabilities for analysis of the mechanical behaviour of composite materials. The MATLAB code enables a variety of fibre orientation angles to be generated and a wide variety of fibre volume fractions to be analyzed under mechanical loading. In order to validate the accuracy of prediction results, a commercial grade epoxy resin (Araldite LY-5052) and unidirectional carbon fibre (Torayca T700) were used to fabricate some samples of laminated composites with cross-ply configuration using the hand lay-up method. Experimental results such as elastic modulus, tensile strength as well as elongation at break were compared with the theoretical data extracted from MCC. The theoretical analysis were verified with experimental results for the same type of composites. Although the values were different, excellent agreement  in the trends of the changes was found for the two approaches. Therefore, it was concluded that the MCC is capable of predicting the elastic constants of laminated composites with a high level of confidence for a wide range of fabricating conditions. The results also showed that the tensile properties of composites made with 3-layer were generally greater than those of the other evaluated composites. This kind of behaviour may be explained by bondline defects, which adversely influence the mechanical properties.