The austenitic stainless steel, 304L, is used in the petrochemical, marine, food and nuclear industries, wherever high strength and corrosion resistance is required. During the annealing process of austenitic stainless steels, abnormal grain growth may occur and its mechanical properties undergo a negative influence. Precipitations may be annihilated during the annealing process and this provides the conditions for grain growth to occur. For smaller initial grain sizes, powered by higher driving forces, grain growth occurs faster and further abnormal grain growth may occur depending upon annealing time. The aim of this work is to locate a process latitude within which abnormal grain growth is disabled. In order to define what exactly launches the process of abnormal grain growth and what factors come into play, cylindrical specimens of austenitic stainless steel 304L (Böhler A607, Fe-18Cr-8Ni) are annealed at different temperatures and for varying periods of time. The process latitude should be defined by different annealing cycles, one and two step, with variable parameters such as 900, 1000, 1100 and 1200°C and annealing times varying between 10 minutes and 40 hours. Annealing temperatures at 900°C show that precipitations are not annihilated and so no grain growth occurs even over an extended annealing period. At temperatures over 900°C, precipitations are annihilated and so grain growth is possible. At higher temperatures the start of abnormal grain growth occurs earlier. After short annealing times of 10 to 40 minutes at a starting temperature of 1200°C, two step annealing cycles develop a larger initial grain size for the following step. At 1200°C precipitations and faceted grain boundaries are annihilated. So, for the second annealing cycle at 1000°C abnormal grain growth is disabled for annealing times over 24 hours. The validated cellular automata model shows an excellent correlation between the experimentally determined data and grain growth kinetics based upon considerations of temperature and initial grain size. The solution heat treatment required to inhibit abnormal grain growth at a precise point for a particular delivery is determined by the data obtained at the experimental stage.