View photos of the medicinal plant Bursera microphylla (Elephant tree), profiled in Medicinal Plants of the American Southwest.

Use the leaves and twigs and and not the branches or bark. There’s no medicinal advantage to these parts (no need to unnecessarily damage this endemic small tree). Frankincense and Myrrh are rough medicinal equivalents to Elephant tree.

A passage from Medicinal Plants of the American Southwest:

Lesser known is Elephant tree’s influence over systemic inflammations affecting the joints, muscles, and connective tissues. Undoubtedly here, its chemical relation to Boswellia is at the heart of the matter. Most forms (with the exception of severe osteoarthritis) of chronic joint, connective, and soft tissue pain see some degree of relief with internal tincture/tea applications. Try it for long–standing tendinitis, bursitis, arthritis–like situations, and even fibromyalgia.