With the increasing number of river-crossing pipeline projects, many studies have focused on the safety and stability of embankment slopes in horizontal directional drilling crossing embankment construction. In addition, it is challenging to study the influence of key processes in directional drilling construction on the antisliding stability of embankment slopes. A model of horizontal directional drilling crossing the Shaying River embankment was developed by using the numerical simulation software FLAC3D, and the strength reduction method is used to analyze the antisliding stability of the embankment after crossing the embankment. In this study, the effect of the position of the whipstock point on the antisliding stability of the embankment slope was considered. The analysis shows that when the inclined point is located below the center of the embankment, the anti-sliding stability of the embankment is the most unfavorable, and the construction should try to avoid the whipstock point below the center of the embankment. It was also determined that when the vertical distance between the oblique point and the crest of the embankment is exceeding 13 m, the impact on the antisliding stability of the embankment can be ignored.