Shear wave splitting observations are a commonly used tool for inferring anisotropy and flow within the Earth's interior. Here we present the development and validation of a new technique for imaging anisotropy in the upper mantle using local events—shear wave splitting tomography (SWST). The mantle is parametrized as a 3-D block model of crystallographic orientations with the elastic properties of olivine and orthopyroxene, and both orthorhombic and hexagonal symmetries are tested. To efficiently forward calculate splitting, the Christoffel equation is used to progressively split the horizontal components of a synthetic wavelet in each block of the model, and predicted shear wave splitting parameters are obtained with an eigenvalue minimization technique. Numerically calculated partial derivatives are utilized in a linearized, damped least-squares inversion to solve for a best-fitting model of crystallographic orientations. To account for the non-linear properties of shear wave splitting, the inversion is applied iteratively and partial derivatives are recalculated after each iteration. A starting model that incorporates information from predicted splitting parameters is found by spatially averaging fast directions and the ratio of observed-to-predicted splitting times. Models from inversions utilizing this average starting model reach lower misfit levels than do inversions with a random or uniform starting model. Modelling results using synthetic data from several anisotropic structures (i.e. sharp lateral and vertical variations in anisotropy) both within an idealized and a real (Nicaragua–Costa Rica) subduction zone illustrate the capabilities and limitations of SWST. With a station spacing of 25 km in an idealized subduction zone containing uniformly spaced events down to 225 km, both the azimuth and dip of crystallographic axes are resolvable to a depth of 100–150 km and lateral heterogeneities in anisotropy on a scale of 50 km at arc and forearc distances from the trench are retrieved. Spatial resolution of anisotropy at scales of 75 km is possible further into the backarc above 150 km depth. The geometry of stations and observed seismicity in the Nicaragua–Costa Rica subduction zone yields partial to good resolution at scales of 50–75 km beneath the forearc, arc and limited regions of the backarc down to 100 km, and resolution at coarser scales is possible in wider regions beneath the backarc. Given the distributions of seismic sources within many subduction zones and the advances in broad-band seismic array deployments, this new method offers a powerful means with which to constrain the orientation of anisotropic fabric in the upper mantle.