Every material changes its failure behavior under different loading rates, and this is the so-called rate dependency of materials. In particular, brittle and quasi-brittle materials show significant change of strength and strain capacity under different loading rates. Usually this phenomenon can be found experimentally, and this effect can be utilized in many engineering aspects. Thus, formulas based on experimental results have been adopted to predict material failure behavior under a given loading rate in engineering design. Most of the parameters are expressed through diagrams as functions of strain rate. Therefore, if the strain rates are assigned for a certain application of materials, the dynamic factors can be picked from the curve. The strength under the given loading rate can be defined as a factor which multiplies the strength under a quasi-static loading condition. However, this method depends on massive experimental works, and there is still a lack of understanding of fundamental behavior of the material failure characteristics. In this paper, the fundamental failure behavior of brittle material under different loading rates is observed using a numerical simulation based on the molecular dynamics analysis. A brittle material is modeled by numerous particles with a multi-scale analysis scheme. Each particle has interactions with the other particles with Lennard-Jones potential between particles. Sub-million particles are modeled for a simulation. Numerical simulations are performed with different loading rates in a direct tensile test on specimen with a notch. The loading rates are varied over a broad range which includes the stress wave velocity of the material. The trend of the strain capacity curve and crack propagation profile can be achieved from the simulations with various loading rates. The results will provide a detailed description of failure mechanism which changes with different strain rates.