Compressive strength is a crucial and fundamental mechanical characteristic of concrete that is regarded as one of the key factors in several design codes and standards. Timely and precise estimation of it can result in both time and money saving. The implementation of particle packing theories, which have significant potential for improving concrete performance, has been restricted because of the intricate and time-consuming nature of the necessary computations. Hence in this study, the impact of packing density on strength aspect is studied by using Modified Toufar Model (MTM) with machine learning (ML). This model aims to maximize the density of aggregate proportions to minimize the void ratio, which is crucial for meeting the specified standards for compressive strength. The model is trained using a comprehensive dataset of 324 samples that includes specific combinations of concrete, each with known compressive strength values in relation with packing density. The study highlights the impressive accuracy of different ML models in forecasting concrete strength using MTM packing density, as evidenced by highest R2 value of 0.820 and 0.810 by both Random Forest and Gradient Boosting algorithms. Achieving a more efficient and reliable approach for estimating concrete compressive strength is accomplished by integrating particle packing theory and machine learning.