In the present paper, we consider a thermodynamic model using the contact kinematics developed by A. Curnier et al involving unilateral contact, adhesion and Coulomb friction between two homogeneous, isotropic and hyperelastic bodies. Adhesion is described by an internal state variable β^ϕ introduced by M. Frémond. Taking the case of contact between a hyperelastic solid and a plane support, we formulate the associated boundary value problem as a minimization problem when no friction is involved. When the intensity of the adhesion obeys a `static' law, we obtain an existence result for this problem.