AbstractThe advent of pixelated detectors for time‐of‐flight neutron transmission experiments has raised significant interest in terms of the potential for tomographic reconstructions of triaxial strain distributions. A recent publication by Lionheart and Withers [WRB Lionheart and PJ Withers, “Diffraction tomography of strain”, Inverse Problems, v31:045005, 2015] has demonstrated that reconstruction is not possible in the general sense; however, various special cases may exist. In this paper, we outline a process by which it is possible to tomographically reconstruct average triaxial elastic strains within individual particles in a granular assembly from a series of Bragg edge strain measurements. This algorithm is tested on simulated data in two and three dimensions and is shown to be capable of rejecting Gaussian measurement noise. Sources of systematic error that may present problems in an experimental implementation are briefly discussed.