In order to promote the application of explosives in penetration and explosion warhead, the quasi-static mechanical properties of HMX-based pressed high energy bonded explosive (PBX) and DNAN-based melt-cast explosive were studied by universal material testing machine. The stress-strain test data of the two explosives were obtained in the strain rate range of 2.0×10-5 s-1 to 1.0×10-3 s-1. The results show that the mechanical properties of the two kinds of explosives have obvious strain rate effect, but the failure strain of the former is about 6 times of the latter, showing a big difference. Based on the phenomenological method, the exponential hardening constitutive model was established to describe the one-dimensional quasi-static compressive mechanical behavior of the two kinds of explosives, and the parameters of the constitutive model were fitted. The comparison between the calculated results of the model and the experimental results shows that the error is less than 3%, which is in good agreement. The results can provide a reference for describing the mechanical behavior of the two explosives.