Abstract: The yield surface of a hierarchical single surface (HISS) model is a single smooth function, which overcomes the singularity of the so-called cap model. The HISS model with non-associated flow rule and isotropic hardening was introduced, and the influence of main parameters on the yield surface was also investigated. Tests on one Gauss Point were produced by MATLAB, and the stress path and yield surface were measured during a loading process. Based on the further development platform provided by ABAQUS, the HISS model was programmed into a three dimensional user-material subroutine (UMAT). Four kinds of triaxial tests (HC, CTC, TC and TE) of Leighton Buzzard sand were simulated by ABAQUS with the developed model. The stress-strain relationship and volumetric change obtained by ABAQUS were compared with experiments results. The numerical predictions showed a good agreement with the observed behaviours in experiments, which proved the applicability of a HISS model to sands. The model was used to simulate the plate loading test of a layered road bed. The three dimensional implementation of an HISS model in ABAQUS provides the commercial FEM code with a new optional constitutive law for the elasto-plastic problems in soil mechanics.