Analytical solutions of vertical dynamic impedance and velocity response at pile cap for vibration of friction pile in saturated viscoelastic half-space foundation were obtained and verified by considering plain strain model and mixed boundary condition of pile-soil interface as well as effect of excitation frequency based on Boer's porous medium theory for a deeper comprehension of its vertical vibration characteristics. Furthermore，effects of pile depth ratio and permeability coefficient on vertical dynamic impedance and velocity response at pile cap were discussed by parametric comparative analyses. The solutions and results of vertical dynamic impedance and velocity response at pile cap derived diversified the theories of pile dynamics and provided technical references and theoretical support for related engineering practice.