A micromechanical model was used to simulate the mechanical behaviour, the transformation kinetic and the texture evolutions of a 304 stainless steel, deformed by tensile tests at T=-60 degrees C. When the transformation strain is calculated with the phenomenological theory, the model does not very well predict the observed transformation rate and the texture evolution of the main y grain orientations. XRD and EBSD analyses show that the martensitic transformation of y phase into alpha' martensite involves the intermediate epsilon phase. From these observations, new simulations were performed in which only the y ->epsilon transformation strain is considered in competition with classical plasticity of austenite. The alpha' variants were calculated in a second step, from the E variants selected in the micromechanical model. Among the 6 potential a' variants able to nucleate from the same a variant, the best oriented ones, with respect to the applied stress were selected. Under these conditions, the numerical simulations reproduce the experimental results in a more satisfying way.