Two test problems, each the impact of a right circular cylinder on a target plate of finite thickness, at a velocity in the ballistic range, are solved using an Eulerian computer program, HELP, for the solution of axisymmetric time-dependent flows. Test Problem Number 1 is an iron-on-iron impact and Test Problem Number 2 is an iron projectile impacting aluminum. In all cases the materials are treated as compressible and deviatoric stresses are obtained using an elastic-plastic constitutive equation. Computed results from these first two HELP problems are given in considerable detail in order that quantitative comparisons of these solutions can be made with Lagrangian calculations being performed by other research teams.