An analytical solution for the contact between a rigid sphere and a thin composite laminate supported on a rigid substrate is presented. The contact force-deformation, including damage effects, is obtained from an axisymmetric formulation of the contact problem. The material is assumed to be transversely isotropic and following an elastic-perfectly plastic stress-strain law. Damage is predicted using a maximum shear failure criterion. Experimental data previously reported in the literature agree well with the analysis.