Abstract: Three-dimensional slope stability analysis methods and the search for the critical slip surface in three dimensions have always been hotspots in the field of slope engineering. Aiming at the problems that the contribution of the intermediate principal stress to the strength of geotechnical materials is not reflected in the Mohr-Coulomb failure criterion and that the search method for the three-dimensional critical slip surface is not mature, the three-dimensional slope stability analysis method based on unified strength and the search for the egg-shaped critical slip surface are carried out. By embedding the unified strength into the three-dimensional slope stability analysis method for constructing the normal stress over the slip surface, a three-dimensional slope stability analysis method based on unified strength is established. Assuming that the three-dimensional slip surface is egg-shaped, the egg-shaped slip surface equation is constructed, and the particle swarm optimization algorithm is adopted to search for the critical slip surface in three dimensions. The rationality of the method is verified by examples. The results show that the safety factor based on unified strength is higher than that based on Mohr-Coulomb strength, and the increase is positively correlated with the b value, with the maximum increase reaching 20.63%; the shape of the critical egg-shaped slip surface is unaffected by the two strength criteria; the safety factor of the egg-shaped slip surface is 0.24% to 5.00% lower than that of the ellipsoidal slip surface. This method is applied to a practical slope engineering example with remarkable effect. The method not only enriches the three-dimensional limit equilibrium method but also provides a reference for similar projects.