The flexural performances of a rubber concrete beam and a ordinary concrete beam are studied under concentrated load through the experiment. The influences of the content of the rubber powder in the rubber concrete beam on the bearing capacity and the crack width of beams are analyzed. The experimental results show that the crack distributions on two beam surfaces possess the characteristics of self-similar in statistical sense. The maximum crack width of the rubber concrete beam is less than that of the ordinary concrete beam under the same load level. The performance of anti-crack of the concrete beam is improved by adding the crumb rubber. Using the fractal theory, the fractal dimension values of the surface crack of the beams under different load grades are calculated and the relationship between the fractal dimension and the maximum crack width of the surface cracks is established.