The frictionless normal contact of elasto-plastic and rigid spheres is studied numerically by using finite elements. The material of the spheres is assumed to obey \(J\)-flow theory with isotropic hardening and with total strains described by a piecewise-linear (or power) law. Numerous indentation maps are evaluated and discussed for a wide range of geometric and physical parameters. These maps could be important for the constitutive modelling of powder composites.