The aim of the presented work is to develop a deterministic and a probabilistic Cellular Automata (CA) model to reflect the grain growth process for the solution annealing of austenitic stainless steel 304L (18-9 Cr-Ni, balance Fe). This uncontrolled exaggerated grain growth results in a negative influence on mechanical properties, e.g. strength, of the material. In order to define what exactly launches the process of abnormal grain growth and what factors come into play, un-deformed cylindrical specimens were annealed at different temperatures (900°C-1200°C). At higher temperatures the start of abnormal grains occurred earlier. The un-deformed homogenized initial grain structures investigated by transmission electron microscopy proved the occurrence of faceted and rough grain boundaries, explaining higher mobilities of some grain boundaries and occurrence of abnormal grain growth. The solution annealing was carried out at 900°C, 1000°C, 1100°C and 1200°C for annealing times up to 40 hours. Abnormal grain growth started at 1200°C after 120 minutes, at 1100°C after 8 hours, at 1000°C after 12 hours and never at 900°C, due to grain boundary pinning resulting from the carbide precipitations on grain boundaries. Simulated and experimental grain structures are comparable, and simulated results are very close to the underlying physics. Many physical parameters can be taken into account in both CA models. The grain growth process is not only demonstrated qualitatively but also used for a quantitative analysis of grain growth phenomena. Beginning from the predictions of average normal and abnormal grain sizes, then defining the grain sizes separating normal and abnormal grains, and an accurate description of grain size distributions are demonstrated. In the analysis of the simulated grain structure, the start of abnormal grain growth and improved definition of exact fraction of abnormal grains is evaluated. Especially an improved description of grain size distributions by incorporating a two parameter approach for the evaluation of grain size separating normal and abnormal grains, paves the way for an exact description of the grain growth process.