Elemental sulfur (S0) is commonly stored in aboveground blocks formed by pouring molten S0 in thin lifts. The long-term storage of S0 blocks is a potential source of high acidity effluent as a result of the oxidation of S0 to H2SO4, resulting in effluent waters with low pH and elevated SO42− concentrations. These blocks are currently managed during operations within a secure, engineered, containment facility. Characterization of the accessibility of the S0 block to O2 and water ingress is required to fully understand the generation of H2SO4 within the block. The O2 and water ingress are defined by the gas (Kg) and liquid (Kl) conductivity of the S0 block. We present the results of in situ gas pumping tests in vertical and angled boreholes conducted on an aboveground S0 block to determine Kg within the block and to indirectly determine Kl. The Kg test results showed that the block is highly conductive in both the horizontal (geometric mean = 2.3 × 10−4 m s−1) and vertical (geometric mean = 1.7 × 10−5 m s−1) directions and heterogeneous with respect to Kg. Results of the cross-hole tests were considered to yield more representative estimates of bulk Kg than single-well tests because cross-hole tests are relatively insensitive to high head loss associated with turbulent flow conditions that develop near the borehole. In addition, numerical modeling of cross-hole test data provided insight into the anisotropic nature of Kg of the S0 block. Corresponding values of anisotropic Kl computed from Kg were 2.6 × 10−3 m s−1 (horizontal) and 1.9 × 10−4 m s−1 (vertical). Given that S0 blocks are constructed in a similar manner throughout the world, the results of this study should be generally applicable to other S0 blocks.