In this paper, a semi-analytical method for creep investigation and elastic behavior of FGM rotary cylinders has been introduced. Assumed cylinder was divided to numerous _nite width layers with constant thermodynamic properties in each layer. Governing equations converted to ordinary differential equations with constant coefficients by applying continuity conditions between layers and boundary conditions of disc in derived equations, then these equations could be solved by a prepared computer code. For thermo-elastic part, variation of dimensionless radial and circumferential strains versus dimensionless radius investigated for several power of FGM material. Also, verification of results was done. For creep part, variation of dimensionless radial and circumferential strain rates versus dimensionless radius was studied for different temperatures and limited timeframe. Changes of radial and circumferential strain rates versus radius were investigated and the results were validated. Finally, the effects of various parameters on creep behavior of rotary cylinder in several examples was examined.