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The high dependency on oil and gas, leads the exploration and efficiency of the drilling process to be very demanding. Most of the tests conducted to study drill string nonlinearities and failures are performed by simulations on models derived for the purpose. Hence, mathematical modeling of a process is usually the first step taken to understand and analyze the dynamics of any process. Most of the mathematical models of the small scale experimental set ups of drilling rigs are developed by analytical modeling. This paper intends to project the use of Black box modelling procedure as a better, simpler and accurate alternate to analytical modeling. An auto regressive moving average exogenous (ARMAX) model is designed for the drill string experimental set up. The method of converging to the selected model using correlation tests and analyzing the prediction error graphs are discussed in the paper in detail. The least squares method provides unbiased estimates of the process model coefficients. The attraction of the method lies in the fact that the nonlinearities exhibited by the process will also be included in the model, without increasing the complexity or a change in the method used to converge to obtain the model.