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In the present work, the generalized thermoelastic interactions in a hollow cylinder with one relaxation time are considered. The modulus of elasticity are taking as function of temperature. Due to the nonlinearity of the governing equations, finite element method is adopted to solve such problem. The exact solution in the case of temperature-independent is discussed explicitly. Numerical results for the temperature distribution, displacement and radial and hoop stresses represented graphically. The accuracy of the finite element method validated by comparing between the finite element and exact solutions for temperature-independent.