Fine grains are required for Alloy 718 to obtain its high strength. Since grain size is strongly affected by forging conditions, many trial forgings are generally needed. On the other hand. grain size predictions by several simulations have been tried to reduce trial forgings. The purpose of this study is to predict grain size of Alloy 718 by combining a numerical simulation and a physical simulation. Firstly the transitions of temperature and strain of the forged material during hot forging were calculated by the 3-dimensional FEM. Secondly multi-stage plane strain compression tests using small test pieces were carried out by means of the Gleeble system according to the temperature and strain programs obtained by the numerical simulation, then the grain size was observed. These simulations were applied for predicting and refining the grain size of Alloy 718 billet forged by hydraulic 4-ram radial forging machine. Introduction Fine grains are required for Alloy 718 disks mainly used for gas turbines to obtain its high strength. To obtain the fine grain disks, it is necessary to refine the grains of the billets of which the disks are made by means of die forging. But it is difficult to refine the grains of large section size billets, especially at center position (1,2).Alloy 718 billets have been generally forged by 2-ram press or 4-ram mechanical radial forging machine (GFM) (1-8). In this study, 4-ram hydraulic radial forging machine, called SMX (by SMS EUMUCO Inc.), was used to forge Alloy 718 billets. SMX has advantages over the 2-ram press; its forging speed is higher and straighter and more truly round billet can be obtained. SMX also has advantages over GFM. The maximum load can be added throughout the full stroke by SMX whereas it can be added near the only bottom dead point by GFM. So the reduction in pass of SMX can be controlled, although that of GFM must be set a small value. Therefore SMX can easily control the forging conditions. These advantages are effective to obtain fine grains of all the regions of large section size billets.On the other hand, since grain size is strongly affected by the forging conditions, many trial forgings, which are very expensive especially for the high price materials such as Ni base superalloys and take much time, are generally needed to control the microstructure. Therefore grain size predictions by several simulations have been tried to reduce trial forgings (1,2:4-8). FEM (Finite Element Method) has been used to predict the strain and the temperature distribution and the microstructure including the grain size of forged products. Not only 2-dimensional FEM but also 3-dimensional FEM must be used for the forging by 2-ram press and 4-ram press, because the deformation behavior of these forgings is complicated. But grain size predictions only by FEM or other equations are difficult for highly-alloyed metals, because the grain growth and recrystallization behavior is very complicated. Especially, the grain sizes of Alloy 718 are strongly affected by the precipita...