This paper, which is the second in a two-part study, uses a specific boundary-value problem to illustrate some of the features of the theory discussed in the first part. Here, the spherically symmetric deformation of a hollow sphere which has a traction-free inner wall and a prescribed radial displacement δ at its outer wall is studied. The analysis is carried out within the small-strain theory of nonlinear elasticity and the body is assumed to be composed of an elastic material which is homogeneous and isotropic, and which has a linear response in shear and a trilinear response in dilatation.For a certain range of values of the applied displacement δ, the problem has an infinity of solutions and these describe configurations which involve a phase boundary; the strain field is continuous on either side of the phase boundary but suffers a jump discontinuity across it. A “kinetic law”, which is a supplementary constitutive law pertaining to particles located on the phase boundary and relating the driving traction on the phase boundary to its velocity, is then imposed, leading to a unique response in all quasi-static motions.As δ increases monotonically during a quasi-static motion, the hoop stress at the cavity first increases, then decreases discontinuously as the phase boundary emerges from the cavity wall, next increases slowly (or, for certain special kinetic laws, remains constant) as the phase boundary propagates outwards, and finally commences to increase at the original rate once the body has been fully transformed.