The volume fraction equations of five-equation-reduced model were studied and numerical scheme was developed in two-dimensional Eulerian frame in planar and cylindrical geometry. To capture material interfaces, Yang's slope modification of artificial compression method was adopted in MUSCL, PPM and WENO type data reconstruction processes. HLLC-HLLCM hybrid flux was applied in Godunov type scheme to avoid numerical shock instability. For multi-material Riemann problems, numerical results show that the scheme captures shock and contact discontinuities with non-oscillatory character. No numerical shock instabilities growing shows as small perturbations was adding on initial physical variables. SOD problems in cylindrical and spherical geometries and contact-type two-dimensional Riemann problem were studied.