We describe and model GPS measurements of surface deformation from the Oaxaca segment of the Mexican subduction zone to characterize interseismic strain accumulation and episodic transient slip in this region and test seismologically-based models of strain accumulation and release along subduction interfaces. Deformation measured from 2001 to 2007 within our dense 31-station GPS array has consisted of (1) trench-normal horizontal contraction at rates that decrease monotonically inland from the coast, (2) rapid coastal subsidence that changes gradually to slow uplift at locations more than 100 km inland and (3) periods of transient slip that interrupt the otherwise steady deformation. Inverse modelling of transient station offsets in 2004 and 2006 indicates that transient slip along the subduction interface occurred downdip from the rupture limits of previous large earthquakes in this region in both 2004 and 2006. GPS site velocities that are corrected for the effects of this transient slip vary significantly over distances of only tens of kilometres both along the coastline and inland, implying that similar spatial variations occur in the degree of locking across the subduction interface. Deformation rates measured along the coast reach their maximum above the core of the rupture zone of the shallow-thrust earthquake and generally decrease outwards towards the edges of the rupture zone. Bounded-value, inverse modelling of the interseismic GPS velocity field with a finite element mesh that simulates the study region indicates that much of the rupture zone of the 1978 shallow-thrust earthquake is fully locked at the plate convergence rate, but that this region is surrounded by weakly locked areas of the subduction interface, which may slow or arrest the propagation of future earthquakes. Much of the deeper region of transient slip, downdip from the seismogenic zone, is also fully locked between the episodes of transient slip; however, the elastic energy that accumulated due to locking of this deeper transitional zone between 2002 and 2006 appears to have been mostly or completed released by the 2004 and early 2006 transient slip events. The approximately balanced energy budget for the deeper zone of transient slip implies that this region is unlikely to contribute significant elastic energy to future earthquakes that originate along the seismogenic zone. Our results support a model in which seismic asperities coincide with regions of strong locking between earthquakes. The potential elastic energy that has re-accumulated since 1978 in the seismogenic zone is already sufficient to cause a repeat of the 1978 earthquake. [ABSTRACT FROM AUTHOR]