The third continuity condition required is the continuity of the stress component normal to the interface between the fibre and matrix, that is,

(7.182)

Using, Equation (7.171) and the unknown constants in above condition, we get

(7.183)

The unknown constants   and

(7.183)

can be determined from the first of Equation (7.180) and Equation (7.183) along with additional equations that will result due to the application of specific load or deformation, which in turn will depend upon which of the engineering property is to be determined.

Let us write the strain displacement relations for fibre and matrix using Equation (7.172) and Equation (7.175) through Equation (7.177).

(7.184)

Note that the strains in the fibre are spatially uniform.
           
Using above relation in Equation (7.171) we get the stresses in fibre and matrix as

(7.185)

From the above equation, it is easy to see that like strains, the stresses are also spatially uniform in the fibre. Further, the radial and hoop/transverse stresses are identical for this case.