So far, I have mainly mentioned 3-dimensionai analysis. Of course the various achievement is highly notable in other method. Skin pass rolling was referred to in some researches before~(21)), but analysis for it has highly developed as 2-dimensional problems. For example, Orowan's~(57)) and Karman's~(80)) method for elastic-plastic materials considering the flattening of rolls, analysis based on continuum theory of dislocasion~(73)) have been reported recently. This is expected to be solved as 3-dimensional problem and the analysis will make clear the cause of C-camber based on unsymmetrical phenomena in upper and lower. Although analysis for complicated 3-dimensional deformation has become possible by FEM, it is undesirable that there is the difference among calculations by concrete method from the viewpoint of requiring reliable information. In this sense we should evaluate the organization of research sub-committee for theoretical analysis under the rolling theory committee. This sub-committee carried out bench mark test and this will be the first step to practical use of the theory. Considering numerical simulation in practical processing, reliable input data are important. It is a long time since Nadai~(35)) presented the way of representing interfacial frictional resistance and it has been discussed lately~(70)). However, it is still difficult to fix the data and we have not gotten the key for the solution yet. Furthermore it is important to adopt accurate deformation resistance of work materials because measuring it in hot working condition is difficult. A calculation~(48)) states that about 17 percent difference of deformation resistance arises the difference of stress by three times at a certain point in roll gap. In summary, this means that it is necessary to construct the data base for simulations in order to raise the value of theory, furthermore data basing these calculations would be beneficial to simulation of whole process such as operating condition. Theoretical analysis on processing problems has gone far toward development and improvement of technology, especially in the rolling process. I hope that further development of theoretical analysis on the rolling process will last as ever before.
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