Aiming at the random non-homogeneous media thermoelastic axisymmetric problem

and under the random Weibull and exponential distributions

a new method to solving the random probability distribution using the expression of continuous function is provided; and the analytical solutions are attained in the plane strain and plane stress model. The numerical experiment

discussing the change rule of thermal stress random distribution parameter m

indicates that there is distinct difference between non-homogeneous media themal stress and homogeneous media thermal stress in Weibull

but little difference in exponential distribution.