The cylindrical or terete and spineless stems of Euphorbia arceuthobioides may be grey-green or yellow-green as here. They taper notably between base and tip, often branching much, also higher up. Branches are mostly smooth, occasionally showing a rough patch, a laterally compressed tubercle where the ephemeral, deciduous leaves had grown.
While mature plants have many branched stems, most plants appear few-stemmed and sparsely branched with spiky thin stem tips. In the absence of leaves (which is most of the time), the plant is usually unable to cast much of a shadow. Branches sprout opposite each other on the stems, well spaced and at right angles to the previous pair.
This plant was seen in midsummer heat, long after the short-lived triangular leaves on new growth of the last winter had fallen. The rudimentary leaves grow opposite and are sessile or nearly so (Vlok and Schutte-Vlok, 2010; iSpot; Bond and Goldblatt, 1984; JSTOR).