This article describes the observed and examined effect of crumb rubber on the strength (compressive, bending and splitting tensile) of concrete. The tests have shown that the change in the strength of concrete with crumb rubber waste additives can be forecasted from exponential equations. These relationships enable to foresee the regularities of strength properties when a certain amount of crumb rubber of a certain size fraction is added to concrete. The obtained exponential equations show that concrete compressive, flexural and splitting tensile strengths decrease with increasing crumbed rubber additive amount. The testing has also shown that the addition of a small amount of crumbed rubber slightly increases (7%) the tensile splitting strength. The reason is better adhesion of the cement stone with rubber particles compared to the adhesion of sand, which was replaced by crumbed rubber. With higher content of crumbed rubber additive in the concrete, the tensile splitting strength decreases due to the significant increase of entrained air content and lower density.