The paper is concerned with a particular case of stress amplification arising from the proximity of a spherical cavity to the boundary of a loaded elastic solid. The performed approximate analysis yields distributions of stresses and displacements in the narrow region formed between a spherical cavity and the faces of a thin flat layer subjected to a far field uniform radial tension. The narrow region is modelled as a circular plate of non-uniform thickness undergoing coupled membrane and flexural deformation. Series solutions are obtained for both membrane forces and bending moments leading to estimates for the stress concentration factor at minimum thickness. These predictions are found consistent with those obtained from both the exact analytical solution and finite element modelling of the problem. Cross-validated results from the two latter methods also provide trends for the stress amplification due to the narrowness of the region.