We propose a method to analyze dynamic rupture processes of earthquakes with a dipping fault, using a three-dimensional finite difference (FD) method with nonuniform grid spacing. This approach does not require aligning the fault plane to the FD grid for implementation of the FD method. It can be used to deal with a realistically complex fault geometry model. We validate our method by studying two dynamic source problems that have been analyzed by Madariaga et al. One is the instantaneous rupture of a circular fault embedded in a homogeneous elastic medium; the other is the spontaneous rupture of a rectangular fault which starts from a local circular asperity on the fault plane. Our numerical results for different dipping faults are similar with those obtained by Madariaga et al. using a horizontal fault plane model in full space, thus validating our method for dipping fault models.