  In this article we propose a novel geometric model to study the motion of a
physical flag. In our approach a flag is viewed as an isometric immersion from
the square with values in $\mathbb R^3$ satisfying certain boundary conditions
at the flag pole. Under additional regularity constraints we show that the
space of all such flags carries the structure of an infinite dimensional
manifold and can be viewed as a submanifold of the space of all immersions. In
the second part of the article we equip the space of isometric immersions with
its natural kinetic energy and derive the corresponding equations of motion.
This approach can be viewed in a similar spirit as Arnold's geometric picture
for the motion of an incompressible fluid.
