We reconstructed the three-dimensional (3D) surface displacement field of the 24 August 2014 M6.0 South Napa earthquake using SAR data from the Italian Space Agency’s COSMO-SkyMed and the European Space Agency’s Sentinel-1A satellites. Along-track and cross-track displacements produced with conventional SAR interferometry (InSAR) and multiple-aperture SAR interferometry (MAI) techniques were integrated to retrieve the east, north, and up components of surface deformation. The resulting 3D displacement maps clearly delineated the right-lateral shear motion of the fault rupture with a maximum surface displacement of approximately 45 cm along the fault’s strike, showing the east and north components of the trace particularly clearly. These maps also suggested a better-constrained model for the South Napa earthquake. We determined a strike of approximately 338° and dip of 85° by applying the Okada dislocation model considering a single patch with a homogeneous slip motion. Using the distributed slip model obtained by a linear solution, we estimated that a peak slip of approximately 1.7 m occurred around 4 km depth from the surface. 3D modelling using the retrieved 3D maps helps clarify the fault’s nature and thus characterize its behaviour.