Peripherally clamped thin shallow hyperbolic metal shells under internal pressure are widely used as rupture discs, quick opening devices and the structures in metal plastic processing. In the bulging process of shells, if the corner radius of the up-holder is too large, negative-curvature zone close to boundary will be enlarged. Contrarily, if the radius is too small, shear rupture will happen in the clamped rim. The contact between the shell and the up-holder corner in deformation is explored by elasto-plastic finite element analysis, and the results are verified with experiments. Influence of the up-holder corner on the mechanical behavior of bulging shells is closely related to the non-dimensional parameter ru/s0 (ratio of the corner radius ru to the original thickness s0). The influence can be partitioned into four regions by three demarcation points, ru/s0 = 0.52, 1.50, and 2.00. The four regions are respectively full effect region, unstable region, near-stable region, and no effect region.