Neutron diffraction spectra were recorded during tensile testing of Fe–30.5 at.% Pd shape memory alloy at temperatures above Ms and below Mf. Peak intensity changes indicate that the application of tensile stress to initially fully austenitic material results in the preferential martensitic transformation of grains oriented with austenite 〈100〉 parallel to the tensile axis. Tensile stress applied to initially fully martensitic material causes the greatest extent of reorientation in those variants oriented with martensite 〈001〉 lying parallel to the tensile axis. These results are interpreted using a simple elasticity-based theory. Additionally, diffraction peak shifts provide information on the development of lattice strain in differently oriented grain families during loading. This indicates that above Ms the alloy exhibits high single crystal elastic anisotropy. Below Mf the apparent stiffnesses of different grain families suggest that axially compressive internal stresses develop in those grain families in which most variant reorientation occurs. These stresses act to reverse the variant changes upon subsequent unloading.