Surface discharge initiation and propagation on the surface of an insulating solid immersed in a dielectric liquid were examined numerically and experimentally. To establish a generalized numerical technique for evaluating surface discharge phenomena using the electrohydrodynamics (EHD) approach, we employed the governing equations of EHD, including the Navier-Stokes equations. To these coupled governing equations, we added a temporal surface charge equation for the charge accumulation on a dielectric liquid-solid interface, as well as terms for ionization, dissociation, and recombination effects. To validate our numerical technique, we compared numerical solutions for breakdown voltage and current with the results of the experimental tests of a needle-bar system with a dielectric liquid-solid interface. The calculated propagation speeds of the surface discharge were compared with the experimental values reported in the literature and found to be in good agreement.