A rim material having a non-uniform thickness, a rim manufactured from the rim material, and a method for manufacturing the rim from the rim material. The rim material includes a first material portion which forms an axially curved portion of the rim after the rim material is formed to the rim and a second material portion which forms an intermediate portion between adjacent axially curved portions after the rim material is formed to the rim. The first material portion has a thick parallel-surface portion including opposite surfaces parallel to each other. The parallel-surface portion has a width greater than a maximum amount of an axial dislocation of the parallel-surface portion expected to occur when the parallel-surface portion is formed to a corresponding curved portion. The second material portion has a thickness varying portion. The thickness varying portion includes a surface having a configuration defined by a line including a straight line and/or a slightly curved line.