According to the present researches, the strength of natural clay shows significant anisotropic properties, but its objective laws haven't been verified by rigorous tests. Based on the Hangzhou intact soft clay tests that are finished by hollow cylinder apparatus (HCA), a formula of the anisotropic clay strength for any principal stress directions is proposed to modify the Casagrande formula in this paper. Assuming that the soil slip failure mode follows the Prandtl mechanism, the upper bound solution of stability against basal heave of excavation is presented. Furthermore, the influences on stability against basal heave of excavation caused by the factors such as the anisotropy ratio of soil, the embedded depth of the retaining wall, the thickness of soft clay layer between the foundation base and the underlying hard stratum as well as the wall roughness are discussed. The method proposed in this paper is verified by a case study in Hangzhou basal soil after failure. It is also shown that it would overestimate the safety against basal heave if the anisotropy of strength is ignored or the Casagrande anisotropic strength formula is adopted.