A brace for providing therapeutic pressure to a person's or animal's body part is provided together with a venting device for use with a cast or brace. The brace has a rigid exterior shell which is perforated over a substantial portion of its surface. An interior resilient liner is arranged in the shell and this liner is also perforated. At least a portion of the liner has two inner and outer layers of flexible material and spacer members connecting these layers and forming air passageways. At least the inner layer is porous. The venting device can have two half sections which, when combined together, enclose a body part. Each half section is preformed to closely fit around a curved side of the body part and has spaced-apart inner and outer layers of flexible, material with at least the inner layer being porous. Again, spacer members are arranged between and connect these layers and form air passageways.