This work describes a method for determining material parameters included in recrystallization and grain growth models of metallic materials. The focus is on the recrystallization and grain growth models of Ni-Fe based superalloy, Alloy 718. High temperature compression test data at different strain, strain rate and temperature conditions were chosen to determine the material parameters of the model. The critical strain and dynamically recrystallized grain size and fraction at various process conditions were generated from the microstructural analysis and strain-stress relationships of the compression tests. Also, isothermal heat treatments were utilized to fit the material constants included in the grain growth model. Verification of the determined material parameters is carried out by comparing the average grain size data obtained from other compression tests of the Alloy 718 specimens with the initial grain size of $59.5{mu}m$.