Abstract: Design of experiments is a systematic approach to research planning that enables obtaining the most informative results at the minimum resource costs. In analytical chemistry, mathematical modeling and experimental design methods are increasingly used to optimize the conditions for the extraction of biologically active substances from plant matrices. At the same time, traditional organic solvents are highly toxic and flammable, which stimulates the search for environmentally friendly alternatives. In recent years, more and more attention in this direction has been paid to eutectic solvents (ESs), which are characterized by low toxicity, biodegradability, and high extraction capacity. This paper provides an overview of modern research on the use of mathematical modeling in combination with ESs, as well as an experimental study of the stability of gallic acid as a model phenolic compound with antioxidant and anti-inflammatory activity in a number of hydrophilic ESs based on choline chloride and acids, alcohols, and an amide. It is shown that the stability of gallic acid depends on the nature of the ES components: in the system with urea, the substance rapidly decomposes at temperatures above 45°C and ultrasonic treatment time of more than 10 min, whereas in acidic and alcoholic ESs it remains stable over wider time and temperature ranges. Using an example of extraction from burdock root (Arctium lappa L.) by the response surface method, the optimal parameters are found, i.e., the choline chloride : ethylene glycol system (1 : 2) with 20 wt % of water at 70°C and treatment time of 40 min, at which the yield of gallic acid was 42.7 ± 1.3 µg/g. The coincidence of the experimental and calculated values confirmed the adequacy of the constructed regression model.