Computational and experimental results on the evolution of stresses and deformation fields due to indentation from a rigid spherical indenter on a graded substrate are presented. The analyses address the variations in Young's modulus, E, of the substrate as a function of depth, z, beneath the indented surface for an exponential law, E = E₀e^αz, where E₀ is Young's modulus at the surface and 1 α is a length parameter. The finite element simulations are used to check the analytical theory of Giannakopoulos and Suresh [Int. J. Solids Struct. (in press)], and are used to gain further insights into the effects of the variation in Poisson ratio, v, with depth. The theoretically predicted force-indenter penetration (P-h) curves are also compared with direct experimental measurements made on compositionally graded NiAl₂O₃ and TiAlY₂O₃-stabilized TZP composites of known composition gradients. A new method is proposed for the estimation of Young's modulus variations through a compositionally graded layer by recourse to spherical indentation.