Taking the elastic stage of the cylindrical standard rock specimen under nder homogenized surrounding pressure as the research object, the three-dimensional stress function of the specimen is constructed based on the theory of space axisymmetry of elastic mechanics and the semi-inverse method. According to the stress function, the stress component is deduced. It is convenient for the study of the internal mechanical properties of rock. Compared with the ANSYS simulation results, it is found that the two results are in good agreement with each other, which indicates that the constructed stress function is desirable.