Despite the advancement of medical knowledge and the development of diverse medical and laboratory products for the prevention, treatment or improvement of various diseases, this science still requires more potent drugs and, at the same time, less side effects. Today, due to the proven low side effects of medicinal plants as well as their acceptable strength in the fight against diseases, various pharmaceutical industries are in development with these plants. Also, the need for reliable preservatives in terms of efficiency and health in the food industry and the many uses of livestock from plants with these properties are abundant. Sumac is one of these plants with various properties and compounds such as flavonoids, flavones, tannins, phenolic acids etc. Antibacterial, antifungal, anticancer, anti-diabetic, and several other valuable properties of this plant have been used in modern and traditional ways from a long time ago till now. One of the most valuable compounds with high anti-cancer properties in this plant is gallic acid from the phenolic acid group, which is present in large quantities in this plant. Despite all the properties of this plant in the fields of pharmacy, food industry, animal husbandry, etc., it can be said that due to the abundance of this plant apos;s growth in our country, it is cheap and accessible. Extraction has different types, each of which has strong points, but also limits such as high solvent dissipation, hazardousness, low purity, high time consumption and cost, damage to extractive materials, and so on. Hence, a novel method in extraction science called extraction with super critical solvent significantly reduces these constraints. In this thesis, the extraction of gallic acid from sumac plant was carried out using super critical extraction method with liquid carbon dioxide and ethanol solvent. The reason for using super critical carbon dioxide in this project is the high solubility and viscosity and low surface tension of these conditions and the reason for using this compound (carbon dioxide) is the low pressure and critical temperature points, safety, affordability, availability. In this project, for the extraction of gallic acid from this plant, two factors influencing the laboratory conditions, ie particle size and constant static time (particle size 2 mm and static time of 24 minutes), were considered and four other influential factors Namely, the temperature, pressure, super critical fluid flow and dynamic time were evaluated. The intervals tested here were, for temperature range from 35 to 75 ° C, for pressure from 10 to 30 Pascal, a flow rate of 1 to 2.2 milliliters per minute, and also a dynamic time interval of 60 to 140 minutes. Then, a statistical study of these experiments was carried out using a response procedure (using central cube design) with Minitab software 18. Experiments were carried out at five levels of coding with a total of 31 experiments. Finally, data modeling by this software with a detection coefficient ( 2 R ) of 95.71% and an improved detection coefficient of ( 2 R (adj)) % 95.70, determined the optimal point of the laboratory conditions for the studied areas in this thesis which has a temperature of 35 ° C, a pressure of 30 Pa, a flow of 1.64 ml/min, and a dynamic time of 127.087 minutes. Also, to determine the basis for the amount of gallic acid present in the plant and to compare the extraction results with the super critical method in this project, another extraction method, ie extraction of soxhlet (extraction by solvent) with ethanol solution, was used. The optimal (or maximum) amount of extraction at the optimal point obtained by super critical method was 16.08 mg and the extraction with soxhlet was 30.25 mg, indicating recovery percentages of 53.15 in super critical extraction as compared with solvent extraction. The super critical extraction reduces the disadvantages of time consumption, high solvent dissipation, low purity, etc. for super critical extraction and a large number of similar and different constraints for other methods. Another part of this work is the mathematical modeling of the extraction of gallic acid from the sumac plant. In this modeling, four thermodynamic models PR, SRK, CPA-PR and CPA-SRK were used to determine the equilibrium conditions and to completely solve this model. Finally, the results of the quadruple work were adapted to the experimental results, which led to the selection of the mathematical model by incorporating the CPA-PR thermodynamic model with a 16.7% error rate. In the end, some measurable parameters for gallic acid and carbon dioxide were obtained in this project by optimizing the genetic algorithm. Key words: gallic acid, super critical extraction, sumac, method of response procedure, mathematical and thermodynamic modeling, genetic algorithm