  A metric tree is a tree whose edges are viewed as line segments of positive
length. The Dirac operator on such tree is the operator which operates on each
edge, complemented by the matching conditions at the vertices which were given
by Bolte and Harrison \cite{BolteHarrison2003}. The spectrum of Dirac operator
can be quite different, reflecting geometry of the tree.
  We discuss a special case of trees, namely the so-called regular trees. They
possess a rich group of symmetries. This allows one to construct an orthogonal
decomposition of the space $L^2(\Gamma)$ which reduces the Dirac. Based upon
this decomposition, a detailed spectral analysis of Dirac operator on the
regular metric trees is possible.
