Effects of excitability and coupling strength on plane and spiral waves in two-dimensional excitable lattices modeled by phase-coupled elements are investigated. The corresponding phase diagrams for stable plane waves and spiral waves are obtained by simulations. The parameters capable of supporting stable spiral waves are sorted out together with the spiral rotation frequencies. This discrete model corresponds to an excitable medium with zero refractoriness and in the continuum limit supports zero-core spiral waves. The associated wave propagating behaviors are also discussed analytically and verified.