In this study, the variation of workpiece surface roughness with varying pulse duration, open circuit voltage, wire speed and dielectric fluid pressure was experimentally investigated in Wire Electrical Discharge Machining (WEDM). Brass wire with 0.25 mm diameter and SAE 4140 steel with 10 mm thickness were used as tool and workpiece materials in the experiments, respectively. It is found experimentally that the increasing pulse duration, open circuit voltage and wire speed, increase the surface roughness whereas the increasing dielectric fluid pressure decreases the surface roughness. The variation of workpiece surface roughness with machining parameters is modelled by using a power function. The level of importance of the machining parameters on the workpiece surface roughness is determined by using analysis of variance (ANOVA).