Spiral-wound heat exchangers (SWHEs) have been widely used in chemical production processes. As the equipment becomes larger, the SWHEs start facing the problem of failure caused by the flow-induced vibration (FIV) phenomenon. To assure the safety and reliability of the SWHEs, it is important to understand clearly the natural modes of spirally wound coils in different sizes and their response under external excitation. Therefore, a 3D model of the helix tube is established and the helix tubes are fully investigated. The effects of different geometrical parameters on the frequency and vibration amplitude of the helix tubes are performed at each mode, by using the finite element (FE) method. Then, the vibration amplitude analysis of the helix tube under harmonic excitation is carried out, and the dangerous frequency band of the equipment under different geometrical parameters is obtained, which is mainly around 10 Hz to 40 Hz in current domain. Moreover, sensitivity analysis is presented to have a more in-depth investigation into the effects of vibration deformation and frequency, which shows that the biggest influence factor is the helix angle. Finally, machine learning is used to predict dangerous frequency, then case studies are presented to verify the validity of the regression method in which the random forest (RF) model and extreme gradient boosting (XGBoost) have the smallest error, less than 10%. The results are very important for designing SWHEs on large scale to meet the requirement of industry development.