An expandable bladder for shaping a pneumatic tire to be mounted inside a tire curing press has a pair of opposing annular beads and an expansion portion located 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 have a radius of curvature less than infinity. At a distance (x) from each end of the central portion, the bladder has an increased thickness in the shoulder and upper sidewall portions.