In this work the superplastic behaviour of a hot rolled AZ31 magnesium alloy sheet under a biaxial tension test with the blow forming technique is presented and reported. The specimen dome height and its thickness distribution, during and after the test, have been used as characterizing parameters. A numerical FE model of the test has been developed in order to easily characterize the material and to directly analyze experimental results. The influence of the rolling cycle on the microstructure and consequently on the material behaviour has been also analyzed. A synergic use of experimental results and of the numerical model has been done for finding material constants in different situations. The material flow parameters have been found and results are presented.