Wire electrical discharge machining (WEDM) process is a specialized thermal machining process capable of accurately cutting and machining mechanical parts with various hardnesses and intricate shapes. WEDM is also a modification of electrical discharge machining (EDM) and it has been widely used for a long time for cutting punches and dies, shaped pockets and other machine parts on conductive work materials. The surface roughness of a machined surface mainly depends on the feed rate, the current and pulse duration in the WEDM machining process. It also depends on the optimum selection of WEDM parameters. The present study focused on the multiple regression modeling and predicting the surface roughness of the Dievar hot-work tool steel during the WEDM process. Mathematical relationships between the surface roughness and WEDM cutting parameters (feed rate, current and pulse on time) have been investigated. The results show that the multiple regression analysis is a successful method for developing a mathematical model to predict the surface roughness.