A family of Sigmoidal non-linear models is commonly used to determine the critical period of weed control (CPWC) and acceptable yield loss (AYL) in annual crops. We tried to prove another non-linear model to determine CPWC and AYL in a soybean agroforestry system with kayu putih. The three-year experiment (from 2019–2021) was conducted using a randomised complete block design factorial with five blocks as replications. The treatments comprised weedy and weed-free periods. Non-linear models comprised 45 functions. The results show that the Sigmoidal and Dose-Response Curve (DRC) families were the most suitable for estimating CPWC and AYL. The best fitted non-linear model for weedy and weed-free periods in the dry season used the Sigmoidal family consisting of the Weibull and Richards models, while in the wet season the best fit was obtained using the DRC and Sigmoidal families consisting of the DR-Hill and Richards models, respectively. The CPWC of soybean in the dry season for AYL was 5, 10, and 15%, beginning at 20, 22, and 24 days after emergence (DAE) and ended at 56, 54, and 52 DAE. The AYL in the wet season started at 20, 23, and 26 DAE and ended at 59, 53, and 49 DAE.