Gravity gradient noise generated by seismic displacements may be the limiting factor for the sensitivity of third-generation gravitational wave detectors at frequencies below 10 Hz. A finite element framework has been developed to calculate the soil response to various excitations. The accompanying gravity gradients as a result of the seismic displacement field can then be evaluated. The results of the gravity gradient noise are in good agreement with previous analytical results. Finally results of gravity gradient noise from a single pulse excitation of a homogenous medium are discussed for an underground detector.