Abstract: High vibration and energy consumption in the construction of full face rock tunnel boring machine (TBM) has been a difficult problem researched by experts in the field.Based on the cutterhead structure and through deformation analysis of the cutterhead during TBM construction,cutterhead vibration was divided into two types:longitudinal vibration generated in the TBM excavation direction and torsional vibration generated in the cutterhead rotation direction.Thus,two models were developed:longitudinal free vibration model and torsional free vibration model.After conducting in-depth theoretical research,this paper presents the theory and methods for calculating the natural frequencies of both the longitudinal and torsional free vibrations of the cutterhead,the theory is used to solve for the natural frequencies of longitudinal and torsional vibrations of a TBM cutterhead.It is found that with the cutterhead quality unchanged,cutterhead longitudinal vibration free frequency is the cutterhead bearing radius and cutterhead thickness function;cutterhead torsional vibration free frequency is only the cutterhead thickness function;the minimum exists for the algebraic sum of the natural frequencies of longitudinal and torsional vibrations.The research method and results of the paper provide a theoretical basis and reference for circumventing the violent vibration of the TBM in construction.