The magnetization reversal processes in cylindrical and spherical soft core/hard shell exchange-spring structures are investigated via the analytical nucleation theory and are verified with numerical micromagnetic simulations. At small core sizes, the nucleation of magnetic reversal proceeds via the modified bulging mode, where the transverse component of the magnetization is only semi-coherent in direction and the nucleation field contains a contribution from self-demagnetization. For large core sizes, the modified curling mode, where the magnetization configuration is vortex-like, is favored at nucleation. The preference for the modified curling mode is beneficial in that the flux-closure allows cylindrical and spherical core/shell exchange-spring elements to be densely packed into bulk permanent magnets without affecting the nucleation field, thereby offering the potential for high energy product.