Heat transfer has considerable applications in different industries such as designing of heat exchanger, nuclear reactor cooling, control system for spacecraft, and designing of microelectronics cooling. As the surfaces of two metals contact each other, this issue becomes so crucial. Thermal contact resistance (TCR) is one of the key physical parameters in heat transfer of mentioned surfaces. Measuring the experimental value of TCR in laboratory is highly expensive and difficult. As an alternative, numerical modeling methods could be engaged. In this study, inverse problem method solution is utilized as a proper method for estimation of TCR value. In this order, three different configurations (flat-flat, flat-cylinder, and cylinder-cylinder) were utilized in two steady and unsteady state conditions to predict the value of TCR. A comparison between the measured values and obtained values from the simulation show the errors for flat-flat, flat-cylinder, and cylinder-cylinder configuration after 10min from starting the experiment are 4.6074%, 0.1662%, and 0.5622%, respectively. And in steady-state condition, the corresponding errors are 6.06e-3%, 1.506%, and 0.846%, respectively. In conclusion, the final results establish the fact that the inverse problem method solution can predict TCR values between contacting surfaces.