The challenges of predicting the stresses acting around piles driven in sand limits meaningful analysis of their single and group loading responses, aging processes and scale/in-situ stress level dependency. Benchmark local stresses measurements made in the sand mass and pile shaft in Calibration Chamber (CC) models show that sharply different regimes act when the pile is either penetrating or temporarily stationary. This paper presents an Arbitrary Lagrangian–Eulerian (ALE) finite element simulation of installation into dense sand, highlighting the stress changes developed between intermittent penetration stages and exploring the effects of initial stress level. The installation by cyclic jacking of closed-ended model piles studied in a highly-instrumented CC experiments is simulated with a state-dependent Mohr–Coulomb model calibrated to high-quality element tests on the sand employed. The predicted pile head loads and local stresses are compared with the CC experiments, showing generally good agreement over the lower parts of the pile shaft while also matching key field-scale trends from CPT-based practical design approaches. More advanced constitutive modeling appears necessary to eliminate discrepancies noted over the higher shaft levels, which may be linked to currently neglected aspects of the sands’ highly non-linear behavior, including grain crushing and hysteresis under cyclic loading.