This paper presents a numerical investigation on the mode-I crack propagation in quasibrittle structures under compressive cyclic loading based on a cohesive element model. The constitutive law of cohesive elements consists of a plastic-type model in compression and a strain-softening damage model in tension. Such a constitutive relation leads to the formation of a residual tensile zone at the crack tip upon unloading, which is responsible for cohesive fracture. The proposed model qualitatively agrees with the experimental observations. Furthermore, it is shown that the existing fatigue kinetics equation for tensile fatigue can be extended to compressive fatigue crack growth through a fracture process zone (FPZ) equivalence principle.