•TPC extraction from Azadirachta indica leaves powder.•To understand and establish the useful kinetic expression model by Peleg's model•To optimize and identify significant parameters for maximum extraction yield.•Compare the experimental results with conventional batch extraction methods. The current work deals with ultrasound-assisted extraction (UAE) of the total phenolic compounds (TPC) from A. indica (Neem) leaves powder. Various process parameters have been optimized, including solvent screening, solid/solvent ratio, extraction temperature, particle size, power input, duty cycle, and sound wave frequency. The highest TPC yield of 11.87 mg of GA/g of powder was obtained at a time of 14 min, 70% ethanol as solvent, solid to solvent ratio of 1:30, particle size of 0.2–0.3 mm, extraction temperature of 40ºC, power input of 90 W, and duty cycle of 50%. The experimental outcomes obtained from the UAE have been matched with stirred batch and Soxhlet extraction of TPC, which shows that ultrasound, was relatively better than the traditional method. The UAE method has efficiently decreased the extraction time (14 min) and marginally improved the TPC yield from A. indica leaves. Further, Peleg's mathematical model was studied for the extraction kinetics and to calculate the predicted extraction values of the rate constant, initial rate, and equilibrium concentration for all investigational circumstances. The predicted values obtained from Peleg's mathematical model show a good fit with experimental outcomes. Display omitted