Based on assumption that the density of the material behind the shock front varies as a power function of the radial position, the equations of motion of a viscous, compressible fluid are solved analytically for the flow field in a spherical target which is impacted at hypervelocity by a spherical projectile. Good comparisons are obtained between the present solutions for velocity distribution and normal stress and various available experimental data as well as with another theoretical solution. The influence of viscosity of the material, which is assumed to be constant, on the velocity distribution and normal stress behind the shock is found to be significant after the initial hydrodynamic stage of the impact process.