In this paper, a new analytical method is proposed to generate concrete random aggregate structure (RAS) in meso-scopic level. This method is particular useful for the progressive failure of concrete under various external loads. In the meso-mechanics level, the concrete is taken as the composite material consisting of aggregate, mortar and interface between them. As a result, it is generated a random aggregate structure in which the shape, size and distribution of the aggregate particles resemble real concrete in the statistical sense using the Monte Carlo random sampling principle in this paper, and the method proposed can generate both regular aggregate particles and irregular ones in 2-Dimmension. It is should be noted that vector concept and some controlling measures are also proposed to avoid generating aggregate particles not consistent with real ones. Numerical examples are simulated to validate the proposed method finally.