Digital volume correlation (DVC), the three-dimensional (3D) extension of digital image correlation (DIC), measures internal 3D material displacement fields by correlating intensity patterns within interrogation windows. In recent years DVC algorithms have gained increased attention in experimental mechanics, material science, and biomechanics. In particular, the application of DVC algorithms to quantify cell-induced material deformations has generated a demand for user-friendly, and computationally efficient DVC approaches capable of detecting large, non-linear deformation fields. We address these challenges by presenting a fast iterative digital volume correlation method (FIDVC), which can be run on a personal computer with computation times on the order of 1–2 min. The FIDVC algorithm employs a unique deformation-warping scheme capable of capturing any general non-linear finite deformation. The validation of the FIDVC algorithm shows that our technique provides a unique, fast and effective experimental approach for measuring non-linear 3D deformations with high spatial resolution.