Problems of stress concentration around a spherical cavity in transversely isotropic materials under pure shear are solved by the equivalent inclusion method. A method previously devised for finding the solution requires introducing harmonic functions in three different spheroidal coordinates and this complicates the analysis. Compared with that approach, the present method is simpler and more transparent; any possible error can be easily detected as the solution procedure requires only elementary algebraic manipulations. Stress concentrations around the cavity are obtained in explicit mathematical expressions and maximum hoop stress can be conveniently calculated. Numerical results of several transversely isotropic materials (zinc, magnesium, β-quartz, and poled barium titanate) are tabulated and graphically displayed to highlight the nature of the solution.