Experimental and numerical methods were employed to study deformation mechanism and elastic properties of the plain woven SiO_2f/SiO₂ composite which was prepared by conventional sol-gel process. Firstly, the elastic modulus along the fiber direction was measured experimentally; Secondly, the representative volume element (RVE) method was used to set up the cell model in ABAQUS software. Equivalent elastic modulus of the material was obtained based on periodical boundary condition, and was compared with experiment data to verify the reliability of numerical method. Finally,the nine equivalent elastic constants of SiO_2f/SiO₂ composites were calculated based on FEM analysis results, including Young’s modulus, shear modulus and Poisson ratio. The conclusions can be drawn that the RVE method based on boundary condition can solve the deformation compatibility of RVE method, and be used to predict the elastic property of material and deformation behavior. The prediction equivalent elastic constants agree with the test result and can contribute to structure design and optimization of the advanced SiO2f/SiO2 composites.