The structures and gas-phase acidities (GA) of several CB11H12H-based carborane acid derivatives (HA) have been calculated with DFT B3LYP method using 6-311+G**, 6-311++G** basis sets. In order to verify the obtained GA values, several systems were also studied at G3(MP2) level of theory. Inserted substituents (CF3, F, Cl, Br, I, CN, CH3, etc.) followed the "belts" of the monocarborane cage starting from the boron antipodal to the carbon. In general, the predicted intrinsic gas-phase acidities of the systems varied according to the substituents in the following order of decreasing strength: CF3 > F > Cl > Br > I > CN > CH3. Nevertheless, some inconsistencies occurred. F and CN derivatives with lower degree of substitution had weaker intrinsic acidities than the respective Cl derivatives, but the situation was reversed in the case of a larger number of substituents. To obtain better understanding how the substituents influence the basicity of the carborane anion, three hypothetical reaction series were investigated, in which the protonation center was fixed on the boron atom (B-12), antipodal to the carbon (C-1), and a single substituent replaced the hydrogens at the vertexes of the three remaining positions (C-1, B-2, and B-7). The intrinsic gas-phase acidities in these series of neutral carborane-based acids CB11X1H11H are found to clearly depend on the field-inductive and resonance effects of the substituent X. Some influence of the polarizability of X oil the reaction center (B-12) could be detected only in the alpha position (B-7).