The object of this thesis is to derive a structural equation for mechanical behavior of workpiece at elevated temperature using the measured values in hot rolling mills. In this regard two different methods were used an analytical method and an Artificial Neural Networks. In the first part of this thesis an inverse analysis technique is used to obtain a more accurate prediction for the flow stress in a steel rolling finishing mill. The inverse problem is defined as the minimization of the differences between the experimental measured values and that of the predicted ones by the presented model. The friction condition at roll/work-piece interface is derived from the Bland and Ford model. It is shown that the developed inverse analysis technique is reliable and can simultaneously determine a more accurate flow stress for the material as well as a better estimation for the interface friction factor. In this thesis as a case study and for the practical determination of the flow stress under forming condition in an industrial finishing rolling mill which is performed at real condition at elevated temperatures, the log files of an special steel grade, containing the required parameters such as the rolling speed, rolling force, rolling torque, reduction per pass on workpiece, temperature etc, were used to be utilized in predicting the flow stress of material. To investigate the validity of the present model, the percentage error in predicting the rolling force as one of the most important parameter in controlling the dimensional quality of the product is evaluated. To reduce the calculated error obtained from the analytical method, an artificial neural network model is proposed to predict the flow stress variations during the hot rolling process. In the first step, since the network can only be as accurate as the data and the networks are general and do not have any prior information about the data and since the Feed Forward Artificial Neural Networks FFA have shown good interpolation ability such a network was utilized. Preprocessing includes eliminating wrong data to make sure that the data is correct and normalization of the input and target vectors. Optimization of the proposed neural network with respect to number of neurons within the hidden layer, different training methods and decision functions of the neural network is performed. The proposed FFANN has initial structure of 4-N-1 consisting of three layers with 4 neurons at the input, N neurons in the hidden and one neuron at the output layer. For the training stage, once the network structure and input are determined, then the weights and biases are randomly initialized and FFANN can be trained. During the training process, the data set of input and output were used to adjust the network parameters so that outputs for a given input are as close as possible to the desired output. Commonly, during the training process the weights and biases of the network are iteratively adjusted to minimize the mean square error of the network error. The results of the optimal network were compared with that of the conventional analytic method and it is shown that both the mean calculated error is reduced by employing an optimal neural network by about 50%. Keywords : Flow stress, flat rolling, inverse analysis, least square regression, neural networks, modeling and analysis, optimization.