Abstract: Due to the complicated mechanism of steel lattice girder and sprayed concrete composite supporting structures, it is diffiuclt to conduct a mathematical description directly. An equivalent transverse isotropic model is proposed based on the mechanical equivalent principle, in which the mechanical property in the isotropic plane is the same as that of concrete and the mechanical property in orthogonal direction is the same as the axial mechanical propertiy of the steel lattice girder concrete. According to the principles of strain coordination, strain energy equivalency and strength equivalency, the axial deformation parameters and strength parameters are obtained. Based on the actual mechanical behavior of the steel lattice girder concrete, an equivalent constitutive relation is put forward and the constitutive relation curves are drawn to describe the complex mechanical properties of steel lattice girder concrete indirectly. The numerical comparison proves that the equivalent constitutive relation is well approximated with the elastic mechanical properties of steel lattice girder concrete.