Multi-scale science is the challenge and opportunity of science in the 21th century, and turbulence of liquid and fracture of solid will be the classical problems of multi-scale mechanics. The failure process of brittle materials displayed a multi-scale mechanics feature that amounts of micro damages grow large trans-scale and nonlinear and evolve to a macro catastrophic transition in the end. So, the concepts of scale and hierarchy of material are inescapable in strength theory to be used explaining solid fracture, it is the main puzzle of the strength theory at present. In the paper, in order to show the phenomena of multi-scale fracture, numeric method is used to simulate the failure process of brittle material, during which micro cracks initiate, grow large, aggregate and in the end form a run-through fracture band in the sample. The result of the numeric simulation shows that the micro cracks of a meso-scale size initiate due to tensile strain and the sample of a macro-scale size breaks down due to tensile-shearing strain under uniaxial tensile or due to compression-shearing strain under uniaxial compression. It powerfully disabused the puzzles in teaching strength theory of brittle material. The further discussion concluded that for a brittle material grain of meso-scale size, the theory of Maximum Tensile Strain is reasonable in explaining the strength, as for a brittle material sample of a macro-scale size, the mohr-columb theory is reasonable for its strength owing to the two important factors of cohesive strength and friction factorwere introduced.