The logspiral cone failure mechanism of threedimensional slopes was built based on the upperbound limit analysis method. The present method was verified by comparing the results with the published data of the classical literature. The energy dissipation due to soil volume compression was neglected and the corresponding influence on the stability of threedimensional slopes was investigated. Then, the effects of soil nonhomogeneity on the stability of threedimensional slopes with different inclination angles, internal friction angles and ratios of width to height were explored. The results show that the influence of the energy dissipation due to soil volume compression should be considered when the internal frication angle is large but the inclination angle and the ratio of width to height is small. However, when both the internal friction angle and the inclination angle are large or just the internal friction angle is small, the energy dissipation due to soil volume compression could be neglected. The stability of threedimensional slopes decreases with the increase of nonhomogeneity and the decrease magnitude becomes larger when the slopes have smaller inclination angles or larger internal friction angles. In addition, the threedimensional effects of slopes are reflected by ratios of width to height. Slopes with stronger threedimensional effects are greatly affected by nonhomogeneity. When the nonhomogeneity is very strong, the stability factors of slopes with stronger threedimensional effects are smaller than those of slopes with weaker threedimensional effects.