Technological developments in high-resolution time-of-flight neutron detectors have raised the prospect of tomographic reconstruction of elastic strain fields from Bragg-edge strain images. This approach holds the potential to provide a unique window into the full triaxial stress field within solid samples. Recent work has provided an algorithm to achieve tomographic reconstruction for systems subject to <i>in situ</i> loads in the absence of residual stress. This paper details an experimental proof of concept for this algorithm involving the full reconstruction of a biaxial strain field within a nontrivial steel sample. Aside from a small systematic error present within individual measurements, the experiment was a success and now serves as a practical demonstration of Bragg-edge transmission strain tomography for systems under <i>in situ</i> loads.