In thin sheet the anisotropy of the internal stress due to constraint by the surrounding parent phase which will be abbreviated as “constraint stress,” seems to occur during the martensitic transformation and the variant selection is expected also in the transformation without external stress. To verify this, the textures were measured by X-ray pole figure method on the γ and α phase which were developed in thin sheet of Fe-30 Ni alloy prepared by severe cold rolling and annealing followed by subzero quenching to liquid Nitrogen. Experimental data were analyzed with conventional variant selection models. The results obtained are as follows: (a) Variant selection phenomenon was clearly observed and the results could be explained with conventional variant selection models. (b) It is expected that different results occur between the conventional variant selection models when the martensitic transformation occurs accompanying the strain component of |ε1||ε2|, where ε1 is the strain along the Bain compression axis and ε2 is along the perpendicular axis.