This study investigates the impact of wheel slip, drawbar pull, and soil strength on agricultural tyre sinkage under varying normal loads and inflation pressures. A controlled experiment was conducted using a 13.6–28 bias ply tyre in a soil bin, measuring tyre sinkage, drawbar pull, and wheel slip across different conditions. Machine learning models, including Artificial Neural Network (ANN) and Support Vector Regression (SVR), were developed to predict tyre sinkage based on key variables, with hyperparameter tuning to optimize model performance. The SVR model outperformed the ANN model, achieving an R2 of 0.997 for training and 0.981 for testing, with Mean Squared Errors (MSE) of 0.836 and 4.296, respectively. The Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) were also significantly lower for SVR, with MAPE values of 2.58% (training) and 6.94% (testing). This optimized SVR model was subsequently deployed in a Streamlit web application, enabling real-time, user-friendly predictions of tyre sinkage based on input parameters. This tool has significant potential for enhancing tractive efficiency and minimizing soil degradation in agricultural practices.