The surface roughness influences the mechanical properties of materials, such as elastic modulus, hardness, tensile and yield strengths and ductility. Previous studies have shown the behavior of hardness changes by surface roughness of the material using spherical indenters on the spherical surfaces. The effect of the elastic modulus changes with the roughness, but this has not been truly investigated. The main purpose of this study is to develop a computational methodology to estimate the behavior of elastic modulus and hardness of the material on different surfaces. The models used in this study are developed using the Msc Patran and simulated by a finite element analysis code LS-DYNA. In this study, four models have been developed with different surfaces to estimate the behavior of elastic modulus and hardness by nano-indentation using a sharp tip conical indenter. The change in modulus and roughness are estimated by nano-indentation using the Oliver and Pharr's theory. The penetration depths are normalized as the change in roughness scale on the material and also as the change in radius of the indenter. The study shows that as the roughness of a surface increases, the hardness increases from the actual hardness at various depths, and it carries on a first order model of roughness with a fractal surface material by nano-indentation method. Not only the roughness influences the material properties but also when the material has damage, it also influences the material properties. For this, the models are developed by placing some voids in the material, and the behavior of elastic modulus and hardness of material with and without damage are estimated. Finally, the penetration depth estimated from nano-indentation is compared using the classical macro-scale Hertzian theory, and interestingly found that this theory can also be used for nano-indentation of metals and solids. The results from this research can be utilized to estimate roughness and modulus degradation caused by nano-indentation.