Multiple inverters are connected to the distribution network with complex non-linear loads and may interact with the background harmonics in some cases. In addition to the parallel resonance caused by the harmonic current, the harmonic voltage also causes the series resonance. The matching of frequencies of the resonance voltage and current results in serious distortion of the grid-connected bus voltage waveform, or even threatens the stability of its operating point. A general method to analyze the network series and parallel resonance of multiple grid-connected inverters is yet to be proposed. In view of this, the authors provide an inverter model and an analytical method to traverse all the resonance points. Two typical control inverters were modelled under the transfer function model, and the defects of the traditional modal analysis method in traversing the series resonance were analyzed. Then, the authors propose to use an improved modal analysis method by adding virtual branches for resonance analysis. The obtained analytical results are consistent with the frequency sweeping results and simulation results, verifying the effectiveness of the proposed method. In order to prove the generality of the proposed method for traversing the series and parallel resonance of multiple grid-connected inverters, the inverter to suppress background harmonics of the grid voltage was incorporated into the multiple inverters network for case study. Using the improved modal analysis method to traverse the series and parallel resonance, the participation factor values of each node and loop under resonance mode were calculated. Finally, the proposed method was verified by hardware-in-the-loop simulation, and the result shows its universality.