Transverse vibration of drillpipe in coring drilling is undesirable. Here, the influence of the core on drillpipe vibration is considered for the first time. Attention is focused on the vibrations of the coring drillpipe as these vibrations lead to contact and collision between drillpipe and core. A reduced-order model of drill string motion is established considering fluid load and core constraints. This model considers fluid action as distributed load and drillpipe as beam structure. The constraint of the core on lateral vibration of the drillpipe is simplified as a nonlinear force. The method of multiple scales is used to analyze the disturbance of the drillpipe’s primary resonance and harmonic resonance, and the influence law of different parameters on the drillpipe resonance is obtained. The results show that damping inhibits resonance vibration, and external excitation determines the resonance type. The existence of the core will aggravate the resonance vibration of the drillpipe. The analysis results are helpful in understanding the resonance of the drillpipe in coring drilling. Some measures to suppress resonance are given in this paper. This study can provide guidance for further research on drillpipe resonance in core drilling.