Abstract: For numericalsimulation of wave motion, this paper generalizes the explicitmethod for 1-D wave equation to 2-D case, and develops thecorresponding recursion formulas for an irregular grid for 2-Dwave equations. For uniform quadrate grids, an approach toconstruct 2M-order stable formulas is discussed in detail, withM being a positive integer, which is illustrated by constructingsecond-order (M=1) and fourth-order (M=2) formulas. Bynumerical tests, the theoretical results presented in the paperare demonstrated, in which the effect of highly accurate recursionformulas in improving calculation efficiency is emphasized.