The experimental study presented in this paper aims to select the most suitable cutting and offset parameter combination for the wire electrical discharge machining process in order to get the desired surface roughness value for the machined workpieces. A series of experiments have been performed on 1040 steel material of thicknesses 30, 60 and 80 mm, and on 2379 and 2738 steel materials of thicknesses 30 and 60 mm. The test specimens have been cut by using different cutting and offset parameter combinations of the "Sodick Mark XI A500 EDW" wire electrical discharge machine in the Middle East Technical University CAD/CAM/Robotics Center. The surface roughness of the testpieces has been measured by using a surface roughness measuring device. The related tables and charts have been prepared for 1040, 2379, 2738 steel materials. The tables and charts can be practically used for WEDM parameter selection for the desired workpiece surface roughness. (C) 2000 Elsevier Science Ltd. All rights reserved.