Rapid stress cycling is a complex loading condition that acts with high frequency and high strain rates within an extremely short period. Concrete may be subject to rapid stress cycling under specific circumstances, such as earthquakes or explosions affecting building structures, or military facilities experiencing attacks by military targets. As the primary building material, accounting for approximately 70% of the global construction industry, the study of concrete performance is crucial for ensuring the safety, durability, and sustainable development of building structures. Therefore, an in-depth investigation into the mechanical properties of concrete under rapid stress cycling loading is crucial. This study aims to explore the effects of rapid stress cycling loading on the mechanical properties of concrete using simulation software. To investigate the applicability of constitutive models and the mechanical performance of concrete under rapid stress cycling, this study utilizes two constitutive models, HJC and RHT. The stress-strain relationships and damage characteristics under different first pulse intensities and pulse time intervals are studied. Through numerical simulation studies, it was found that under rapid stress cycling loading, the two constitutive models exhibit different or even opposite mechanical behaviors. The differences in the stress-strain relationships are not significant, while the differences in damage failure modes are more pronounced, with RHT showing higher sensitivity to this complex loading condition.