Abstract: A 100 MeV Hcyclotron, CYCIAE100, is under construction at China Institute of Atomic Energy. To carry out the experimental verification of CYCIAE100, a central region model (CRM) cyclotron was developed for the study on various technical aspects, including the main magnet, beam diagnostics, etc. An optimized multiple linear regression shimming method was investigated based on accurate mapping and bar shimming of the CRM cyclotron. By using the magnet mapping data of CRM cyclotron and the numerical simulation of the field by 3D FEM analysis, the optimized multiple linear regression shimming method was realized and verified. This method is a preresearch for the isochronous magnetic field shimming of CYCIAE100. It can be applied in the isochronous magnetic field shimming of the compact cyclotron, which meets the requirement for beam dynamics analysis.