This paper deals with the transient response of one-dimensional axisymmetri
c quasistatic coupled thermoelastic problems. Laplace transform and finite
difference methods are used to analyze the problems. Using the Laplace tran
sform with respect to time, the general solutions of the governing equation
s are obtained in the transform domain. The solution is obtained by using t
he matrix similarity transformation and inverse Laplace transform. We obtai
n solutions for the temperature and thermal stress distribution in a transi
ent state. Moreover, the computational procedures established in this artic
le can solve the generalized thermoelasticity problem for a multilayered ho
llow cylinder with orthotropic material properties.