The constitutive relation for open-celled metal foams with random characteristics of cells was constructed based on the mechanical behavior and the distribution of the cells, which implied the effect of the mesoscopic characteristics of the cells on the macroscopic behavior of the foam. The constitutive relation was able to represent the whole three phases of the stress-strain curve of the open-celled metal foam with merely one expression. Besides, the explicit expressions for the foam’s yield strain and yield stress were supplied. Experimental data was employed to check the constitutive relation. It was found that the constitutive relation was able to represent accurately the whole compression process of the foams, and the calculated yield points had a good agreement with the experimental results.