This study proposes a method for determination of material characteristics by inverse analysis of free bulging tests results. The blow-forming tests were carried out at the temperature of 415 °C using aluminum alloy (AMg-6) sheets of a 0.92 mm thickness. Each test was performed at constant pressure. For each fixed value of pressure, a series of experiments was carried out with different forming times to obtain evolutions of dome height H and thickness s. Two different constitutive equations were used to describe the dependence of flow stress on the effective strain rate: the Backofen power equation and the Smirnov one taking into account an s-shape of stress-strain rate curve in the logarithmic scale. The constants of these equations were obtained by least squares minimization of deviations between the experimental variations of H and s and ones predicted by a simplified engineering model formulated for this purpose. Using the Smirnov constitutive model to describe the dependence of flow stress on strain rate, unlike the classical power law, makes it possible to analyze the variation of strain rate sensitivity index m with strain rate. On the basis of the obtained data, the optimum strain rate for AMg-6 processing was estimated as one corresponding to the maximum of strain rate sensitivity index. The validity of the proposed method was examined by finite element simulation of free bulging process.