This paper is concerned with the plane train deformation of a hollow cylinder, within the theory of finite elastostatics for a particular homogeneous isotropic compressible material, the so-called Blatz-Ko material. The body is subjected to uniform pressure, either internal or external. In the case of internal pressure, it is found that there is a maximum pressure beyond which there does not exist a solution. Under that pressure there exist two sets of solutions. In the case of external pressure, for a sufficiently large value of pressure, the location of the maximum value of the compressive hoop stress departs from the inner surface ; there exists, however, a supremum of the location. If the hollow cylinder is thinner than the supremum, the maximum value of the compressive hoop stress occurs at the outer surface.