The upper-bound finite element method with rigid translatory moving elements (UBFEM-RTME) is further improved to optimise its suitability for analysing the stability in heterogeneous clay. The method is applied to investigate the stability of the tunnel face in undrained clay layer subjected to surface surcharge. The variation of stability load ?s /cu0 and the morphological characteristics and discipline of the effective discontinuities mechanism are obtained for various combinations of dimensionless buried depth ratio C/D, dimensionless gravity parameter ?D/cu0 and the heterogeneous parameter ?D/cu0. The results reveal that C/D and ?D/cu0 have a significant effect on ?s /cu0 and failure mechanism. ?D/cu0 has a great influence on ?s /cu0 but has little effect on failure mechanism. Furthermore, the UBFEM-RTME is used to show the changes of mesh failure modes under different mesh parameters such as the number and distribution of effective discontinuities, and the reasons for improving the accuracy of the upper bound solution are also explained. The applicability of UBFEM-RTME in heterogeneous clay, especially the analysis of failure mode under the limit state, is verified in comparison with the existing rigid-block upper-bound limit analysis methods and finite element bound method.