The purpose of this thesis is to develop a mathematical model for controlling strip profile and to avoid shape defects in plane strain rolling. To achieve these objects, an extensive study was carried out to examine the suitability of different models for online applications. The slit beam model is employed as a reference model due to its fast performance and precise estimation of the final strip profile. The slit beam defection model allows one to take into consideration the effect of important factors such as; roll wear, roll crown, etc. The numerical method consists of splitting both the backup roll and the work roll span into m equal elements and replacing the load distribution on the roll by a concentrated load applied at the middle of each element. Both profile and flatness are largely determined by the transverse roll gap profile in the finishing mill. To estimate the roll profile of the gap between loaded work rolls, the loads deforming the rolls must be known. Furthermore, it is essential to know the rigid body movement of the work rolls. Considering various methods for predicting the roll deformations, a shape and profile control system is developed with respect to the work roll bending, and roll initial crown. After examining the developed code for the conventional rolling and comparing the results with that of the previous research work an attempt was made to use the slit beam model for the pair cross rolling method. A mathematical model is presented for simulating the pair crossed rolls in roll crossing method, in a four high mill. The top and bottom work rolls and backup rolls are crossed as pairs in same angle values and in opposite direction to change the rolling load distribution between the work rolls along the width and to control the equivalent crown. The equivalent crown is proportional to the square of the plate width. Parameters affecting the strip profile have been accurately identified. Based on this approach a suitable algorithm was developed and a computer code was created. Mill stand dimensions and operating conditions (the required data for the input of the developed code) was obtained from the computer logs of Mobarake Steel Company. Optimum actuators set points for the two methods of controlling the strip crown are obtained for the minimum possible strip output crown, "the jack forces in roll bending method and the cross angle of the rolls in roll crossing method". Consequently, the effective parameters affecting the trend and their values on the final profile of the product are studied and the corresponding graphs are derived. By comparison between the results obtained from the two methods, the crown control capability in roll crossing method is considered to be more effective than the roll bending method especially for the narrow plates. Since, it is was not possible to compare the modeling results with that of the practical information; the prediction accuracy of the presented models is examined by comparison with the existing numerical methods, finite element models and experimental data. It is shown that the present models are in good agreement with the experimental values and other research works in this field. Finally, it can be concluded that a hot rolling mill layout equipped with a pair crossed rolling system is easily able to produce products in high quality and more effectively. Key Words Hot Rolling, Strip Profile Control, Roll Crossing Method, Strip Crown, Slit Beam Model.