As a new material, high modulus asphalt concrete (HMAC) with good durability is widely used in the pavement engineering. One of the most critical performance indexes of HMAC is the fatigue cracking. However, in the experiment of evaluating the fatigue properties, different anti-fatigue effects are obtained only by adding different modifiers. In addition, using only one loading mode to determine the fatigue properties of HMAC neglects the fact that there is a difference among the fatigue test results in various loading modes, which artificially leads to the non-uniqueness and unscientific design of high modulus asphalt pavements for the fatigue resistance. Therefore, four internationally accepted mainstream strength tests at different loading rates, including direct tension, indirect tension, unconfined compression and four-point bending tests, were carried out to enhance the veracity of structural resistance design of high modulus asphalt pavements. It is revealed that the fitted curve for the variation of strength with loading rate is a power function with velocity dependence, and the models for direct tension, indirect tension, unconfined compression, and four-point bending strengths established as a function of loading rate are SD = 3.218v0.1425, ST = 3.833v0.1768, SC = 14.391v0.1130 and SF = 7.839v0.1489 respectively. Besides, it is shown that the conventional S-N fatigue equation does not take into account the velocity dependence of the strength of HMAC in the stress ratios determined by the tests, and the velocity-dependent stress ratios defined in this paper are determined by the strength model and therefore take into account the viscoelasticity of HMAC. In addition, it is found that extending the fatigue curve backwards, when the fatigue life of HMAC is also close to 1, the velocity-dependent stress ratio is 1. Meanwhile, the fatigue model Nf = tv-5.318 was developed by unifying the characterization of HMAC and considering the effect of loading rate in various loading modes. It eliminated the difference of fatigue test results caused by the specimen sizes and loading modes, and effectively improved the completeness of structural design of high modulus asphalt pavements, which provided a theoretical basis for designing the high modulus asphalt pavements.