This paper presents results from large-displacement finite-element analysis of cone penetration into clay. The soil is idealised as a homogeneous elastic-perfectly plastic material obeying a Tresca yield criterion, and the analysis is carried out using an 'arbitrary Lagrangian-Eulerian' technique, with periodic remeshing and interpolation of all field values. This allows the cone to be advanced by several diameters, thus achieving steady-state conditions. A full parametric study has been undertaken, quantifying the influences of the rigidity index, in situ stress anisotropy and the cone roughness. A theoretical correlation for the cone factor, N-kt, is developed from this study, and compared with previous correlations developed using the strain path method. Characteristics of the stress distribution around the cone, the extent of the plastic zone and apparent incremental movements are discussed, allowing new insights into this problem.