This paper deals with the quasi-static coupled thermoelastic problems of an infinitely long rotatingmultilayered hollowcylinder. Laplace transform and finite difference methods are used to analyze problems. Using the Laplace transformwith respect to time, the general solutions of the governing equations are obtained in transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. Also presented are the numerically transient distributions of stress and temperature in the real domain for the case of an infinitely long rotating hollowcylinder composed of three differentmaterials.Moreover, the computational procedures established in this article can solve the generalized thermoelasticity problem for rotating multilayered hollow cylinder with orthotropicmaterial properties.