This paper evaluates the effect of analysis parameter choices on the stability and efficiency of modelling cone penetration into sand. This very large deformation quasi-static boundary-value problem is modelled here using the arbitrary Lagrangian–Eulerian adaptive mesh technique available within Abaqus/Explicit. The sand response is captured using a hypoplastic constitutive model. It is demonstrated that many choices of analysis parameters lead to spurious results, some of which show clear instability, while other combinations show reasonable stability but over-estimation of the cone resistance. The accuracy of the numerical solution is shown through comparison against centrifuge experimental data for two different relative densities of the sand.