The advantages of rubber concrete (RC) are good ductility, fatigue resistance, and impact resistance, but few studies have been conducted on the effects of different rubber admixtures on the strength of RC and the cracking performance of rubber mortar. In this study, the compressive and flexural tests of rubber concrete and the crack resistance test of rubber mortar were carried out by changing the rubber content and adding expansion agent and retarder in this test. The test results show that the strength of RC decreases with the increase in rubber admixture. At 15% of rubber admixture, the expansion agent and retarder increase the compressive strength and flexural strength of RC the most; the compressive strength increased to 116% (22.6 MPa) and 109% (21.2 MPa), and the flexural strength increased to 111% (4.02 MPa) and 116%. (4.21 MPa). At the same rubber admixture, the expander improves the cracking time of the rubber mortar by about 3 times, and the retarder improves the cracking time of the rubber mortar by about 1.6 times. The BP neural network (BPNN) was established to simulate and predict the compressive and flexural strengths of RC with different admixtures and the cracking time of rubber mortar. The simulation results show that the predicted 7-day compressive strength of RC fits best with the actual value, with a value of 0.994, and the predicted 28-day flexural strength was closest to the measured value, with an average relative error of 1.7%. It was shown that the calculation results of the artificial intelligence prediction model are more accurate. The simulation results and test results show that the expander and retarder significantly improve the strength of RC as well as the cracking performance of rubber mortar.