Abstract: Based on the finite element method and the measured data, the uniaxial compression boundary conditions and the elastic parameters of the specimen are obtained by inversion method. Firstly, the parameter inversion equations are derived. Secondly, the surface displacement field of a red sandstone specimen is obtained by the digital speckle correlation method. Finally, based on the grid node displacement calculated by the finite element method and the measured data, the boundary conditions, the elastic modulus and the Poisson's ratio of the specimen are obtained. It is shown that: (1) by using the method developed in this paper, the boundary conditions and the elastic parameters of materials are obtained by the inversion method. (2) the elastic modulus of the specimen is about 18~GPa, and the value is gradually stabilized in the later stage of loading; the Poisson's ratio gradually increases with the loading, and the value is between 0.14 and 0.34. (3) due to the heterogeneous nature of the rock material, a certain difference is observed in the direction and the magnitude of the external load of adjacent nodes in the horizontal direction.