Spiral strand cables are widely used in lightweight cable-supported structures such as sports stadia and bridges. Accurate understanding of their mechanical behaviour is complicated by their complex geometry and the complex contact conditions that exist between the many individual spirally wound wires. This study develops full 3D elasto-plastic finite element (FE) models of the multi-layer spiral strand cables subjected to quasi-static axial loading using LS-DYNA. A novel procedure to generate their complex geometry and FE meshes was devised and two cables with different diameters and numbers of wires were modelled in detail. The predicted axial load–axial strain curves and failure loads were in good agreement with experimental data.