A theoretical investigation is made to identify the mechanism responsible for the phenomena of rapid flame propagation in a vortex tube. The consideration is based on the inviscid, three-dimensional flow structure that results from hco identical flames steadily propagating away from an (igniting) plane of symmetry within an infinitely long straight Rankine vortex, in which the core is filled with a uniform flammable gas mixture of the same density and temperature as the surrounding unbounded inert gas. A new mechanism is proposed in Part I. Because the radial expansion of vortex tube through thermal expansion across the flame causes the spiraling of axial vortex filaments, a torus of azimuthal vorticity is produced at the shoulder part of the parabola-like flame and the flame tip is convected forward by its induced velocity. A closed form of expression for the steady flame propagation speed is derived from the requirement of single-valued pressure held, which agrees with experimental measurements. In Part II, the proposed mechanism and flame propagation speed expression are validated by numerical simulation.