The non-zero stresses resulting from the displacement field in Equation (7.242) are

(7.246)

The continuity of the stresses in radial direction leads the continuity of the stress  at the interface. This condition becomes

(7.247)

Now, at the outer boundary of the concentric cylinders the displacements must match the following boundary conditions.

(7.248)

Note that from the second and the third of the above condition, we get

(7.249)