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.