Beech wood (Fagus sylvatica L.) is used in a wide range of wood products. However, the influence of the wood’s moisture content on its mechanical functions will affect its structural strength. It would be complicated and time-consuming to experimentally measure wood’s mechanical functions under different moisture contents. Therefore, it is necessary to establish a prediction formula between the moisture content and elastic constants, and then verify whether its mechanical functions within a wide range of moisture content can be studied by using FEM (finite element method). In this study, which was based on experimentation, we studied the influence of a wide range of moisture contents and grain direction on the compressive yield strength, modulus of elasticity and shear modulus of beech wood. The relationship between the moisture content and elastic constants was established; the moisture sensitivities of different elastic parameters were obtained. Ultimately, compression curves under different moisture contents were plotted out, using both FEM and experimentation. According to the results, the interaction of moisture with the grain direction had a significant effect on the elastic constants of wood, with grain direction having a greater effect on the elastic properties than the moisture content. Moreover, the decay function can be used to fit these experimental results well. The elastic constants of beech wood responded differently to the moisture content, depending on whether it was in the longitude or transverse directions. Finally, this study proved the feasibility of using FEM to simulate wood’s compressive performance with a wide range of moisture contents.