Wire-Electrical Discharge Machining (WEDM) is one of the non-conventional machining processes for machining hard to machine electrically conductive materials. It has been increasingly used in industry owing to its distinct advantages over the other cutting technologies. The process can only be employed effectively when all its properties and complexities are well understood. In addition many aspects of this technology require to be fully explored in order to increase its capabilities and cutting performance. This thesis contains an extensive literature review and an experimental work on the investigations of various variables in Wire-EDM. It is a fact that the substantial amount of work has been carried out on Wire-EDM, but a very little research has been reported on the influence of the variables such as the work piece thickness and hardness on various machining responses such as surface roughness, kerf width and material removal rate. Accordingly a detailed experimental investigation is presented in this thesis to study the various cutting performance measures in Wire-EDM over a wide range of variables or process parameters including workpiece thickness and hardness. The influence of all these variables/ control factors/ process parameters on the major cutting performance measures in Wire-EDM have been comprehensively discussed and analyzed under two sets of experiments. In the first set of experiments, the influence of eight variables including thickness has been studied on the machining responses such as kerf width, surface roughness, and VIIDepartment of Industrial and Manufacturing Engineering material removal rate. The workpiece material used was Tungsten Carbide. Eight variables including thickness have been taken with three levels each to determine their influence on the machining responses. In this the Taguchi Orthogonal Array has been used to reduce the number of runs for meaningful results. Tungsten Carbide workpieces were machined and the requisite response variables were measured. Likewise, in the second set of experiments the same material was taken and hardened to obtain two levels of hardness. The workpiece hardness was taken instead of thickness with four other variables having two levels each. This was done to validate the results of first experiment and also to see the influence of hardness. In both the experiments, ANOVA was carried out after obtaining the responses to determine the significant factors for each response. The result was consistent with the available literature however new facts were discovered in the case of workpiece thickness and hardness. Workpiece thickness appeared to be significant in case of surface roughness only and hardness was found significant in all the three cases. Finally the optimization of the machining responses was carried out using S/N ratio as specified by Taguchi method for the purpose of research papers publications.