A finite element model of bucket foundation embedded in an elastic half-space was established using the finite element software ABAQUS. The accuracy of simulated results of the model was verified by comparing the numerical solution with existing analytical solutions. The influences of different factors on the vertical initial dynamic impedance of bucket foundation and the relationship between initial dynamic impedances of the bucket foundation and shell foundation were studied. The results show that the length-to-diameter ratio and thickness-to-diameter ratio of the bucket foundation, soil Poissons ratio, soil shear modulus, and soil nonhomogeneity have significant influence on the initial impedance, while bucket foundation material has little influence on the initial impedance. The initial impedances of the bucket foundation and shell foundation are nearly the same, and the bucket foundation can be simplified as the shell foundation in simulated calculation.