New materials require the use of advanced technology in manufacturing parts of complex shape. One of the modern non-conventional technology of manufacturing difficult to cut materials is the wire electrical discharge machining (WEDM). The article presents the results of theoretical and experimental research in the influence of the WEDM conditions and parameters on the shape deviation during a rough cut. A numerical model of the dielectric flow in the gap (ANSYS) was developed. The influence of the dielectric velocity field in the gap on the debris evacuation and stability of WEDM process was discussed. Furthermore, response surface methodology (RSM) was used to build empirical models for influence of the wire speed Vd, wire tension force Fn, the volume flow rate of the dielectric Qv on the flatness deviation after the WEDM.