The fundamental complex susceptibilities χ=χ’-jχ‘ are calculated from the symmetric critical‐state hysteresis loops M(H) for an infinitely long hard superconductor with a rectangular cross section 2a×2b (a≤b). For the critical‐state model, the Bean, the Kim, the exponential law, and the triangular‐pulse local‐internal‐field‐dependent critical‐current densities Jc(Hi) are chosen. The results of χ’ and χ‘ are given as functions of the field amplitude Hm normalized to the full‐penetration field Hp, the sample dimensional ratio a/b, and the p parameter that characterizes the Hi nonuniformity in the sample at H = Hp on the initial M(H) curve. χ‘(-χ’) curves are also given for the different functional Jc(Hi) and other conditions. These theoretical critical‐state susceptibilities are particularly useful in the study of sintered high‐Tc superconductors. For these materials, the procedures to determine the effective grain volume fraction f*g and the averaged and the local intergranular critical‐current densities 〈Jc〉acs and Jc(Hi) by means of ac susceptibility measurements using such theoretical critical‐state‐susceptibility functions are described. Related problems met in the high‐Tc superconductor study such as sample performance nonuniformity, frequency dependence, grain clusters, and susceptibilities for the grains are discussed.