Abstract: A numerical scheme for solving transient two-phase flows in interior ballistics is induced accordingto the theory of space-time conservation element and solution element(CE/SE) method under the transformed coordinates. The ignition process oftwo-dimensional two-phase flows is studied by the CE/SE method. Compared with theexperimental data, the numerical results simulate the actual process. At the initial phase of ignition, a steep pressure gradientexists along the radial and axial directions in barrel chamber. When all thepropellants are ignited, the pressure gradient in the radial directionvanishes. It shows that the two-dimensional CE/SE method is effective forsolving transient two-phase flows in guns.