In order to investigate the interaction of rubber particles and straw powder coupling on concrete mechanics, the rubber particle mixing, straw powder mixing, and silane coupling agent KH570 modification as the three main factors were compared through a compressive strength test. Results show that when rubber particles were added with 10%, 20%, and 30% volume fractions, the compressive strength of rubber concrete was 42.45 MPa, 36.82 MPa, and 30.25 MPa, respectively, which decreased by 15.4%, 26.6%, and 39.7% compared with ordinary concrete, respectively. And the addition of straw powder also has adverse effects on the compressive strength of concrete. The uniaxial compressive damage constitutive model was proposed for modified recycled rubber-straw powder concrete based on the analysis of the entire compressive stress-strain curve, which fits well with the experimental test data. Furthermore, the numerical simulation of the proposed model is conducted using the FEA software ABAQUS, predicting properties such as compressive strength for modified recycled rubber-straw powder concrete with other admixtures.