<p>A longitudinal coupled vibration model of the pile–soil system was constructed using fractional derivatives to modify the Zener standard rheological solid model, accounting for the instantaneous rheological effect of saturated clay around the pile. The frequency-domain analytical solution of the system dynamic control equation was derived using the Laplace transform and potential function decomposition method, and the time-domain response was then obtained under instantaneous excitation at the pile top through Laplace numerical inversion. The effectiveness of the proposed method was verified using degradation models and finite element models. Then, numerical examples were used to analyze the frequency domain characteristics of the dynamic stiffness and damping of pile foundations in rheological saturated clay formations, as well as the wave response under instantaneous excitation at the pile top. The rheological effect of the soil reduced the amplitude of fluctuations in the dynamic stiffness and damping of pile foundations in the frequency domain. Stronger soil rheological properties were associated with a slower rate of increase in the dynamic stiffness and damping of pile foundations with increasing frequency.</p>