The mechanical behaviors of an elastic body containing another materials are studied with the statistical method since they are generally distributed at random in size, orientation, and position. As the basis of this research, the size, the shape, and the ratio of volume for another material assumed to be constant, and only the positions of another material are changed randomly. The stress intensity factor, the compliance, and the modulus of elasticity are investigated in two-dimensional state by using the Monte Carlo Method and the Finite Element Method. The methodology of the simulation analysis for the mechanical behavior of such material is also proposed.