  Volume transition of an inflating cylindrical balloon made of rubber under
external force $F$ is studied based on the non-linear elastic theory for
rubber. The pressure difference $\Delta P$ between inside and outside of the
balloon is calculated as a function of the volume $V$ of the fluid inside the
balloon. It is shown that if $F$ is smaller than a critical value $F_c$, the
inflation of the balloon takes place with coexistence of strongly inflated
region and weakly inflated region, while if $F$ is larger than $F_c$, the
inflation takes place uniformly. It is shown that the critical force $F_c$
depends on the material parameter of the rubber, and that the discontinuous
transition for finite stretching force can take place only when the rubber has
enough stretchability
