The objective of this work is to study the mechanics of indentation of an adhesively bonded layered solid. To this end, several (plane strain) finite element simulations of wedge indentation of a ductile strip which is adhesively bonded to a rigid substrate are conducted by varying the properties of the adhesive layer. The stress fields below the indenter tip and at the strip-adhesive interface are examined for various depths of indentation. The effects of the adhesive properties on the above features of the finite element solution, as well as on the hardness versus penetration characteristics, are investigated. The above results are also compared with those for an unbonded strip resting on a frictionless surface. It is found that once yielding commences in the adhesive layer, the state of stress in it is comprised of a shear stress and a superposed hydrostatic compression. Also, it is observed that increasing the yield strength of the adhesive layer significantly delays the onset of the decreasing phase of the hardness versus penetration curve, whereas, changing the elastic modulus of the adhesive has negligible effect on it.