The microring resonator coupled with the input/output channel waveguides can be applied in filter due to its compactness, functionality, and the possibility of dense integration. In order to achieve flatter tops and sharper rolloff in the passband, the multiple-ring higher order structure is employed. Both the transfer functions of “series-coupled” and “parallel-coupled” multi-ring high order filters are derived using the transfer matrix method. For the “parallel-coupled” structure, the symmetric spectral response is achieved by optimizing the ring distance, while for the “series-coupled” structure, the performance is determined by the coupling coefficients between the ring and ring. In order to obtain maximally flat response passbands, the numerical results show that the proper coupling coefficients should be symmetric and smaller in the middle of the structure.