The boundary-value problem (BVP) resulting from the equations of nonlinear elastostatics for torsion of a circular cylinder for a class of general Blatz-Ko materials is considered. Using a topological shooting argument, the existence of a solution to this BVP is proven, and two-sided a priori bounds implying that the tube must contract radially are given. Previous studies have considered special cases, that is, slightly compressible materials or nearly isochoric deformations. The present results place no such restrictions on compressibility or strain.