Abstract: In a cylinderical coordinate system, integrated gradient method is an effective discrctization for equations of Lagrangian hydrodynamics. In the method IGT (Integral Gradient Total) scheme does not preserve spherical symmetry while IGA (Integral Gradient Average) scheme overcomes nonsymmetry in cylinderical coordinate system. However, IGA results in abnormally large acceleration in case of large mass ratios, where the mass of one subcell around a node is smaller than that of the other three subcells. If boundary force between neighbouring cells is taken as weighted mass average, IGA scheme is equivalent to IGT scheme in both a planar problem and a cylinderical problem even if there exists a large mass ratio. It is shown that IGT scheme preserves total momentum conservation but IGA scheme does not. Numerical results demonstrate advantages and disadvantages of the two schemes.