This paper investigates the degradation of the mechanical properties of concretes made with three types of aggregate affected by alkali-silica reaction (ASR). Three standard testing methods - ASTM C289, JASS 5N T-603 and ASTM C1260 - were used to identify the reactivity of ASR of the three aggregates selected. The test results show that all three aggregates are potentially deleterious. A new acceleration method based on JASS 5N T-603 and ASTM C1260 was proposed for concrete specimens. In the acceleration method, cylindrical concrete specimens were used, additional alkali material was added to the concrete mixture and the specimens were stored under conditions similar to ASTM C1260. The preconditioned concrete specimens were then used for evaluating the mechanical properties of the ASR-affected concrete in terms of strength and stiffness. The test results show that special attention must be paid to the effects of two opposing mechanisms on the strength and stiffness of concrete: hydration reactions and ASR. Hydration reactions enhance the mechanical properties, whereas ASR does the opposite. The changes in length of concrete specimens were also measured, which showed that the basic trends for change in length and mechanical properties may be different. It is better to examine the effect of ASR on both change in length and mechanical properties. The size and reactivity of the aggregate are very important factors for the mechanical properties of ASR-affected concretes. Within the two-month testing period, the reactive fine aggregate might cause ASR expansion and the reactive coarse aggregates might not.