Abstract: In this paper, based on the non-linearly geometric theory for extensible elastic rods, an exact mathematical model of thermal post-buckling behavior of uniformly heated elastic rods with clamped-simply supported ends is derived. This is a two-end point boundary value problem of first-order ordinary differential equations with strong non-linearity and multiple unknown functions, in which the arc length s(x) as one of the unknown functions is involved. By using shooting method and analytical continuation, the non-linear boundary value problem is numerically solved and the thermal post-buckled states of the rods are obtained. The equilibrium paths of thermal post-buckled rods for a variety of the slenderness are given.