A significant variant selection is reported in isothermal martensite formed on the surface of an Fe-30% Ni sample. The selection phenomenon is modelled using different descriptions of the martensitic phase transformation. In particular, matrices based on the phenomenological theory of martensite crystallography, the Jaswon and Wheeler distortion, and the continuous face centred cubic-body centred cubic distortion are compared. All descriptions allow good predictions of the variant selection. However, the Jaswon and Wheeler distortion and the continuous distortion better account for other features of the surface martensite, such as the {225} habit plane and the accommodation mechanism by twin-related variant pairing.