Abstract: Instability of non-uniform deformations of an incompressiblethermo-hyperelastic tube, subjected to internal pressure and axial stretch,is examined within the framework of finite elasticity. When the inflationpressure is small, a thin-walled tube undergoes a uniform inflation. Butwhen the inflation pressure is larger than a certain critical value, thethin-walled tube undergoes a strikingly non-uniform deformation. One partbecomes highly distended as a bubble while the rest remains lightlyinflated. But a thick-walled tube always undergoes a uniform inflationeven if the pressure attains a very high value. A critical thickness for thetube to have an instability deformation is given based on the deformation curves along with its slope. Furthermore, theeffect of axial stretch and temperature on the deformation is discussed.