Heterogeneous pressure-carrying medium was employed to establish a differentiated pressure field on sheet metal in flexible die forming process in this work, which aimed at matching the non-symmetric shape of target component and improving metal inflow to avoid local tensile instability. Specifically, metal inflow corresponding to the differentiated pressure field was analytically evaluated. Forming of a typical non-symmetric shell component was experimentally and numerically studied based on the proposed method. Compared with forming processes based on the uniform pressure, difference of metal inflow in two sides of the non-symmetric component increased from 2.16 mm to 3.36 mm and metal inflow in critical region increased by 11.9% when differentiated pressure field (taking heterogeneous elastomer #4–3 for example) was employed. The resultant maximum thinning ratio decreased by 4.2% and the uniformity of shell thickness increased by 16.9%. With the decrease of Shore hardness of elastomer in the formed region, stress path in the ready-to-form region transferred towards the bi-axial tension stress state, i.e., stress ratio (α) increased. And, stress triaxiality (η) in characteristic regions were regulated appropriately, which decreased the risk of tensile instability. It was attributed to the decreased normal pressure and frictional resistance at sheet/elastomer interface in the formed region.