Transient flow inside a hollow shaft of a Gas Turbine engine during sudden engine stop may result in non uniform heat transfer coefficients in the shaft due to flow instability similar to steady Taylor vortex, which may decrease the lifetime of the shaft. In the present study, transient Taylor vortex phenomena inside a suddenly stopped hollow shaft are studied analytically. Flow visualization is also performed to study the shape and onset time of Taylor Vortices for various initial rotational speed.