The accuracy of the symmetry adapted cluster-configuration interaction (SAC-CI) method for calculating hyperfine splitting constants (hfscs) is examined. Two kinds of SAC-CI expansion are performed : one is the SAC-CI(SD-R, DT-R) method in which single and double (double and triple for high-spin multiplicity) excitation operators are included in the linked operators and the other is the SAC-CI (general-R) method in which higher excitation operators are further included. The hfscs for the doublet, triplet, and quartet states of small radicals, OH, CH2, BH2, CH3, and H2O+, calculated by the SAC-CI method compare very well with the full CI results. A convenient configuration selection method, in which both energy and hfsc are used as criteria, is shown to be useful. This method, which is also applicable to the ordinary CI method, is effective for accurate calculations of the hfscs especially for large systems and high-spin systems, where a large number of configurations are required. Finally, the basis-set dependence of the hfscs is examined using the configuration selection method developed here. Within the Gaussian set, the improvement in energy does not necessarily result in the improvement of the hfscs. We have to use the basis set which satisfies the cusp condition, as shown previously.