Computation of the elasto-plastic solution of ball indentation was carried out by the quadratic programming method. The problem was formulated as an elasto-plastic contact problem under the assumption of small displacement and small deformation and then transformed into a minimization problem. Finite element approximation resulted in a quadratic programming problem. Numerical and experimental study were done with aluminium Al 2024-T351 and commercially pure copper. The computed load-displacement curves were in good agrement with those obtained from experiments. Tabors relationship for representative strains was also examined. Stress distributions were found to resemble closely those results available in the literature.