An integrated mathematical model is proposed to predict the velocity field and strain distribution during multi-pass plate hot rolling.This model is a part of the mixed analytical-numerical method(ANM)aiming at prediction of deformation variables,temperature and microstructure evolution for plate hot rolling.First a velocity field with undetermined coefficients is developed according to the principle of volume constancy and characteristics of metal flow during rolling,and then it is solved by minimizing the total energy consumption rate.Meanwhile a thermal model coupling with the plastic deformation is exploited through series function solution to determine temperature distribution and calculate the flow stress.After that,strain rate field is calculated through geometric equations and strain field is derived by means of difference method.This model is employed in simulation of an industrial seven-pass plate hot rolling process.The velocity field result and strain field result are in good agreement with that from FEM simulation.Furthermore,the rolling force and temperature agree well with the measured ones.The comparisons verify the validity of the presented method.The calculation of temperature,strain and strain rate are helpful in predicting microstructure.Above all,the greatest advantage of the presented method is the high efficiency,it only takes 12 s to simulate a seven-pass schedule,so it is more efficient than other numerical methods such as FEM. An integrated mathematical model is proposed to predict the velocity field and strain distribution during multi-pass plate hot rolling. This model is a part of the mixed analytical-numerical method (ANM) aiming at prediction of deformation variables, temperature and microstructure evolution for plate hot rolling. First a velocity field with undetermined coefficients is developed according to the principle of volume constancy and characteristics of metal flow during rolling, and then it is solved by minimizing the total energy consumption rate. Meanwhile while a thermal model coupling with the plastic deformation is exploited through series function solution to determine temperature distribution and calculate the flow stress. After that, the strain rate field is calculated through geometric equations and strain field is derived by means of difference method. This model is employed in simulation of an industrial seven-pass plate hot rolling process. velocity field result and strain field result are in go od agreement with that from FEM simulation. Stillrther, the rolling force and temperature agree well with the measured ones. The comparisons verify the validity of the presented method. The calculation of temperature, strain and strain rates are helpful in predicting microstructure. Above all, the greatest advantage of the presented method is the high efficiency, it only takes 12 s to simulate a seven-pass schedule, so it is more efficient than other numerical methods such as FEM.