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Structural cables are widely adopted around the world in offshore construction, sports stadia, large scale bridges, Ferris wheels and suspended canopy and fabric structures. However, the robustness of such structures to blast or impact is uncertain with a particular concern related to the loss of a primary structural cable when damaged by high velocity blast fragmentation. This paper presents the first ever numerical and experimental study on commonly used high-strength steel spiral strand cables subjected to high velocity fragment impact. Spiral strand cables were impacted by 20 mm fragment simulating projectiles travelling at velocities between 200 and 1400 m/s. Complex 3D non-linear finite element models were developed and carefully compared with experimental tests. The penetration resistance of the cables and resultant damage were studied with respect to fragment impact velocity. It was found that for all the impact velocities, the fragment penetration depth was less than half of the cable diameter demonstrating a considerable amount of resilience. Considering the damage caused, the residual cable breaking strengths were estimated and found to be still higher than the minimum breaking load of an un-damaged cable. The numerical models were also able to reproduce the main features of the impact tests, including the extent of localised damage area, the fragment penetration depth and mode of individual wire failures, thus demonstrating their potential to be widely used in industry for structural resilience and robustness assessments by structural engineers.