A speedily developed numerical method called as finite volume method (FVM),which possesses both merits of finite difference method and finite element method,is devoloped.The construction of FVM for conservation laws is introduced.Especially,some efficient and successful schemes for solving the discontinuous problems are discussed in detail.Moreover,several numerical results of simulation of 2D dam break problem are given.Finally,a summary of advances in numerical applications and theoretical analysis of FVM is presented.