In this paper, an inverse bi-harmonic axisymmetric elasticity problem is solved by invoking measured out-of-plane surface deformation values at discrete locations around a preloaded bolt head, in order to calculate the underhead contact stress and joint clamp load that would have caused that out-of-plane surface deformation. Solution of this type of inverse problem promises to improve the automation process of bolted joint system assembly, especially in critical and safety related applications. For example, a real-time optically measured joint surface deformation can be utilized for automating process control of bolted joint assembly in a reliable fashion. This would be a significant reliability improvement as compared to the commonly used method in mass production using torque-only control method in which there is wide scatter in the torque-tension correlation due to the normal scatter in frictional variables. Finite Element Analysis (FEA) method is used to validate the inverse problem solution provided in this paper.