Microperforated panels (MPPs) are next-generation absorption materials because they can provide wideband sound absorption without fibrous materials and can be composed of diverse materials to meet global environmental demands. The fundamental absorbing mechanism is Helmholtz-resonance absorption due to perforations and an air cavity. MPPs are typically backed by rigid flat walls, but to reduce the restrictions on the MPP absorber properties, one of the authors has proposed MPP space sound absorbers without backing structures, including three-dimensional cylindrical microperforated panel space absorbers (CMSAs). Advantages of MPPs without backing structures are design flexibility and ease of use. Besides, the absorption characteristics of a CMSA with a core, which has a rigid cylindrical core inside the CMSA, have been experimentally tested, but a method to predict the absorption characteristics is necessary to design CMSAs with cores. Herein the two-dimensional combined Helmholtz integral formulation method is employed, and its prediction accuracy is evaluated by comparing the measured and predicted absorption characteristics of a CMSA with a core. Furthermore, a parametric study with regard to the core size is carried out to investigate the transition of the absorbing mechanism.