By modeling soil as a three-dimensional axisymmetric model and considering the three-dimensional wave effect of soil, a theoretical study is conducted on the frequency domain characteristics of longitudinal vibration of threaded piles in viscoelastic foundations. Based on the three-dimensional wave theory, the wave equation of the soil around the pile under axisymmetric conditions is established. The vibration response solution of the screw pile under fully coupled pile soil conditions is obtained using Laplace transformation and variable separation methods. The results show that compared to the calculation method that ignores radial displacement, the solution that considers the three-dimensional wave effect of soil can take into account the wave effects of longitudinal and shear waves in the soil, with higher accuracy. In the low-frequency range, the longer the length of the screw pile, the greater the dynamic stiffness and damping, and the more significant the effect of the lateral frictional resistance on the sidewall. The smaller the spacing between the screw teeth, the stronger the restraining effect of the soil around the pile on the pile foundation, and the significantly increased vertical bearing capacity of the pile foundation. The existence of the screw teeth has an undeniable impact on the vibration of the screw pile.