Abstract: Riemann problems in three-pieces, which only contains contact discontinuities on initial data, are dassified for 2-D gas dynamics systems, and numerical solutions of the Riemann problems are presented by using Taylor-FVM MInB difference schemes derived in 1.From the numerical results, it is shown that Riemann problem in three-pleas is the simplest cases in Riernann problems for 2-D gas dynamics systems, and the solution structure is basic one.