This study investigates the modeling and single-objective optimization of surface roughness (Ra) and material removal rate (MRR) in electrical discharge machining (EDM) of external cylindrical surfaces of hardened 90CrSi tool steel. The machining process is enhanced using ultrasonic vibration assistance and graphite electrodes to improve surface integrity and productivity. Gaussian Process Regression (GPR) and Response Surface Methodology (RSM) were employed to construct predictive models for Ra and MRR based on key process parameters, including vibration amplitude (A), pulse-on time (Ton), pulse-off time (Toff), peak current (IP), and servo voltage (SV). The GPR model provided superior predictive performance for surface roughness, while RSM was more effective in modeling MRR. Optimization results showed that the minimum Ra of 1.6216 µm was achieved at A = 2.7743 µm, Ton = 8.0000 µs, Toff = 11.8294 µs, IP = 8.1723 A, and SV = 4.7936 V. Meanwhile, the maximum MRR of 12.1989 g/h was obtained at A = 3.5339 µm, Ton = 16.0000 µs, Toff = 8.0000 µs, IP = 15.0000 A, and SV = 4.0000 V. The findings provide valuable insights into parameter selection for improving EDM performance on external cylindrical surfaces of high-hardness steels.