Explicit solutions are obtained, in terms of modified Bessel functions, for the problems of transverse twisting and of tangential shearing of transversely shear-deformable shallow spherical shells with a small circular hole. The relevant stress concentration factors are calculated for the entire range of a rise-to-thickness ratio parameter and a transverse shear deformability parameter. The modification of known results obtained previously by shear deformable plate theory, and by shallow shell theory without consideration of transverse shear deformation effects, is delineated.