Abstract: For the time-dependent behavior of rock-socketed pile groups, the finite element method is utilized to discretize the pile group into singles and pile elements, and the global stiffness matrix equation of the pile group can be obtained by assembling the pile elements simulated by the three-nodal axial rod. Then, the fractional Merchant model and the fractional Poyting-Thomson model are introduced to describe the viscoelastic characteristics of the overlying soil layer and saturated soft rock, respectively. Based on the coupling equation of the interaction between the saturated rock-soil mass and the rock-socketed pile group, and the equilibrium condition and the compatibility condition of pile cap, the matrix solution of the top reaction force of each single pile and the displacement of the cap is derived. Combining Li's analogy method and the Laplace transformation technology, the solution to the time-dependent behavior of vertically loaded rock-socketed pile group is finally obtained. Some examples are designed to discuss the influence of the fractional order and the viscoelastic parameter of rock mass on the time-dependent behavior of the pile group, showing that the deformation of the pile cap and the top reaction force of each pile in rock-socketed pile group gradually increases over time and eventually stabilize.