Abstract: The development of the discrete state space models for computer control and operation optimization of reheat furnaces is presented in this paper. The model development is based on the two-dimensional partial differential equations describing the unsteady-state heat conductions and the corresponding boundary conditions of the heated slabs, which finally are converted to a large-scale discrete state space model with a series of interconnected subsystems through using the techniques of system decomposition and discretization. Real-time dynamic responses of the temperature profiles for any slabs at any positions in the furnaces, geometric size and grade of the steel slabs and their moving rate in the furnace can be provided based on the measurable furnace zone temperatures by the models. The industrial experimental results show that the models' precision is good enough to satisfy the engineering demands. The Mathematical model based hierachical computer control strategies for reheat furnaces are also proposed in this paper.