Spark plasma sintering processes have been rapidly introduced recently to improve the quality and productivity of ceramic products and to solve the problem of environmental pollutions. Sintering temperatures and pressing pressures in the spark plasma sintering process are known to be the important factors highly affecting the quality of the ceramics. In this research, in order to see the effects of sintering temperatures and pressing pressures on the grain growth during the spark plasma sintering process of $Al_2O_3$ the grain growth processes associated with sintering temperatures and pressing pressures are simulated by the Monte Carlo method (MCM) and the finite element method (FEM). In this Part 1, the formulations for the simulation, which is the theoretical background of Part 2, are introduced.