The onset position of the hydraulic jump formed by a water-impinging jet on an inclined substrate was measured. It was found that the outlined shape at the onset of the hydraulic jump became elliptical with the major axis increasing as the inclination angle of the substrate increased. A set of equations were proposed for predicting the onset position of the hydraulic jump. The prediction can be made with a reasonable accuracy, within +/-13% errors, so that these equations can be used to estimate the onset position of the hydraulic jump on an inclined substrate. Moreover, it is also possible to determine the appropriate inclination angle of the substrate and the flow rate of a water-impinging jet for detaching fine particles from an inclined substrate.