Shot peening is a process wherein the surface of a material is impacted by small, spherical metal shots at high velocity to create residual stresses. Nickel-based superalloy is a material with high strength and hardness along with excellent corrosion and fatigue resistance, and it is therefore used in nuclear power plants and aerospace applications. The application of shot peening to INCONEL, a nickel-based superalloy, has been actively researched, and the measurement of residual stresses has been studied as well. Previous studies have used methods such as perforation strain gauge analysis and X-ray diffraction (XRD) to measure residual stress, which can be evaluated with high accuracy, but doing so damages the specimen and involves critical risks to operator safety due to radiation. On the other hand, ultrasonic testing (UT), which utilizes ultrasonic wave, has the advantage of relatively low unit cost and short test time. One UT method, minimum reflection measurement, uses Rayleigh waves to evaluate the properties of material surfaces. Therefore, the present study utilized ultrasonic minimum reflectivity measurements to evaluate the residual stresses in INCONEL specimens. Specifically, this study utilized ultrasonic minimum reflection measurements to evaluate the residual stress in INCONEL 718 specimens. Moreover, an estimation equation was assumed using exponential functions to estimate the residual stress with depth using the obtained data, and an optimization problem was solved to determine it. Finally, to evaluate the estimated residual stress graph, the residual stress of the specimen was measured and compared using the XRD method.