Efficient and reliable dynamic modelling and analysis is critical to the shape control and estimate of a backbone continuum manipulator. This paper presents a novel dynamic modelling method to investigate the deformation modal properties of a vertical stretch-retractable continuum manipulator (VSRCM) under the tip horizontal load. Based on the equivalence of the elastic bending potential energy, this method simplifies the backbone continuum manipulator to a single beam, an equivalent-guided beam (EGB). One end of the EGB is fixed, and the other end is guided. The modal dynamics model of the EGB is then established by employing the vibration theory of a continuous beam, and the modal properties of the continuum manipulator are analyzed. Static and Dynamic experiments of the VSRCM are performed to validate the dynamic modeling method through the comparison and analysis of the free dynamic response and frequency properties of the continuum manipulator. To analyze the free dynamic response, the large deflection static model with tip horizontal load is also established based on the elliptic integral approach. Experimental results and comparison demonstrate that the static model is efficient and precise to predict the large deformation, and the modal dynamic models well reflect the actual vibration modal characteristics of the VSRCM.