A therapy wrap for treatment of at least a portion of an animate body having improved kink resistance. The therapy wrap may be selectively reinforced for improved kink resistance in only a portion of the wrap. The reinforcement may decrease the kink radius. The wrap may include a kink reducer in all or only a selected kink-prone region. The kink reducer may be selectively configured attachment points or spot welds. The therapy wrap may include a reinforcement layer of one or more discrete reinforcement members. The wrap may be formed by pre-tensioning the material layers while forming the fluid bladder and/or gas pressure bladder. The therapy wrap may be adapted to compensate for conditions that normally cause kinking of the wrap or buckling of the fluidic channels. Also disclosed are methods of manufacturing the wrap and methods of administering a temperature-controlled treatment to an anatomical body part.