Despite the enormous amount of concrete consumed, fundamental understanding on the structural properties of hydrated oxides in concrete is still an open question. Due to the structural hierarchies and heterogeneous characteristics of concrete, accurate experimental and theoretical studies have not been well-developed for measuring mechanical properties of crystalline and amorphous materials in concrete. Lack of the information makes the development of constitutive relation of them to the macroscopic concrete properties difficult. The objective of this thesis is to compute mechanical properties of various phases in concrete. Unconventional methods of high pressure x-ray diffraction, absorption, and first-principles calculation are applied to calcium silicate hydrates (tobermorite 14 Å, 11 Å, 9 Å, and jennite), calcium aluminate hydrates (hemi-carboalumiante, monocarboaluminate, strätlingite, and hydrogarnet), tricalcium aluminate, and alkali-silica reaction gel. From the systematic comparison of both experiment and simulation, a comprehensive understanding of structural mechanism is achieved. For tobermorites, interlayer thickness which is related to the number of interlayer water molecules determines its compressibility. Hemicarboalumiante and strätlingite shows a pressure-induced dehydration while monocarboaluminate with the full occupancy of carbon oxide group behaves stable and incompressible under pressure. In the cases of tobermorite 14 Å and monocarboaluminate, linear density approximation in the first-principles calculation predicts the experimentally measured bulk modulus with high accuracy. Based on the excellent agreement of bulk moduli between experiment and simulation, it can be concluded that computed elastic properties of shear and Young's modulus, Poisson's ratio, and elastic tensor coefficients are highly reliable. In addition, combining x-ray diffraction and absorption methods allows accurate measurement of density variation under pressure which is used to compute the bulk modulus of alkali-silica reaction gel.The fundamental structural properties obtained in both experiments and simulations given in this thesis will pave a path toward not just to increase our knowledge of the structural mechanism of concrete but also to optimize concrete design for better structural performance