Based on Timoshenko beam deformation theory,the governing equations for the problem were built up.The authors studied the similarities of governing equations between the homogeneous beam and the non-uniform beam,and then the problem of functional gradient materials beam bending was to solve bending of uniform beam and to calculate similarity coefficient of product.Through theoretical derivation and analysis of the similarity,we found that the bending solutions of functional gradient Timoshenko beam is proportional to uniform materials Timoshenko beam with the same size,boundary conditions and load conditions,This proportional factor was determined entirely by nature inhomogeneous parameter of material constants.