Abstract: For infinite-length functionally graded piezoelectric/piezomagnetic (FGPEPM) hollow cylinders, the statics of the electro-magnetic-elastic coupling for an axisymmetric hollow cylinder is studied. In the cylindrical coordinate system, assuming that the material parameters are distributed along the radial direction as a power function, analytical solutions of the physical fields such as displacement, stress, electric and magnetic potentials in the hollow cylinder under external excitation are derived. In the numerical discussions, for the BaTiO₃-CoFeO₄ composite material hollow cylinder, the distribution of stress, electric and magnetic potentials for the hollow cylinder with different gradient parameters and different thicknesses are obtained under different boundary conditions. The results show that the material failure is mainly caused by the circumferential stress for the FGPEPM hollow cylinder, and that the cylindrical thickness has a significant influence on the circumferential stress. In addition, the gradient parameters strongly affect the electrical/magnetic output and the mechanical properties for FGPEPM sensors/actuators. The results have a certain guiding effect on the design and analysis for FGPEPM cylindrical sensors/actuators.