Rubberized concrete (RC) has received widespread attention due to its energy absorption and crack resistance properties. However, due to its low compressive strength, it is not recommended for structural applications. The rubber size and content affect RC’s mechanical properties. This study investigated and formulated the behavior of RC with different particle sizes and contents under dynamic and static loading. Quasi-static compressive and dynamic tests were conducted on RC with varying content of rubber (0–30%) and rubber sizes (0.1–20 mm). It was found that the rubber particle size was 0.5mm and the rubber content was 2%. An equation was derived from the experimental data to forecast the impact of rubber size and content on compressive strength. Additionally, by combining the literature and this research’s data, a model was established based on neural networks to predict the strength of RC. SHPB tests were carried out to study the stress–strain curves under dynamic load. The peak stress, fragment analysis, and energy absorption of RC with varying content of rubber and rubber sizes at three different strain rates (100 s⁻¹, 160 s⁻¹, and 290 s⁻¹) were investigated. Equations describing the relationship between dynamic increase factor (DIF), rubber material content, and strain rate on different particle sizes were obtained by fitting. The DIF increased as the content of the rubber increased. By analyzing energy absorption data, it was found that the optimal ratio for energy absorption was RC-0.5-30, RC-0.1-30, and RC-10-30 at strain rates of 100 s⁻¹, 160 s⁻¹, and 290 s⁻¹. This study could be a good guideline for other researchers to easily select the content and size of the rubber in RC for their applications. It also has a positive significance in promoting the development of green building materials.