An expandable, toroidal shaped bladder for use in a tire curing press has a pair of opposing annular beads and an expansion portion location between the pair of annular beads. The expansion portion of the bladder has a central portion, shoulder portions, and sidewall portions. When the bladder is in a mounted but uninflated mode, the shoulder portions of the bladder have a radius of curvature R1 significantly less than a radius of curvature Rc of the central portion. The shoulder portions have a bubble or square-like configuration.