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It is commonly assumed that the Gassmann theory (for both isotropic and anisotropic media) is only valid for rocks with interconnected porosity. However, previous theoretical analysis and numerical simulations show that for a wide class of media with disconnected pores or fractures, Gassmann’s theory is valid either exactly or to an accuracy sufficient for practical applications. To explore applicability of the Gassmann theory further, I perform asymptotic analysis and numerical calculations of the deviations from Gassmann theory predictions of the bulk and shear moduli of a material with an isotropic distribution of disconnected spheroidal cracks with and without equant pores. This analysis shows that the Gassmann theory is exact for the bulk but not for the shear modulus of an isotropic system of randomly oriented identical cracks (no pores) but significantly underestimates the bulk modulus of a medium with interconnected pores and isotropically distributed and isolated cracks.