  We make a spectral analysis of the massive Dirac operator in a tubular
neighborhood of an unbounded planar curve,subject to infinite mass boundary
conditions. Under general assumptions on the curvature, we locate the essential
spectrum and derive an effective Hamiltonian on the base curve which
approximates the original operator in the thin-strip limit. We also investigate
the existence of bound states in the non-relativistic limit and give a
geometric quantitative condition for the bound states to exist.
