  A simplified model of the tumor angiogenesis can be described by a
Keller-Segel equation \cite{FrTe,Le,Pe}. The stability of traveling waves for
the one dimensional system has recently been known by \cite{JinLiWa,LiWa}. In
this paper we consider the equation on the two dimensional domain $ (x, y) \in
  \mathbf R \times {\mathbf S^{\lambda}}$ for a small parameter $\lambda>0$
where $ \mathbf S^{\lambda}$ is the circle of perimeter $\lambda$. Then the
equation allows a planar traveling wave solution of invading types. We
establish the nonlinear stability of the traveling wave solution if the initial
perturbation is sufficiently small in a weighted Sobolev space without a
chemical diffusion. When the diffusion is present, we show a linear stability.
Lastly, we prove that any solution with our front conditions eventually becomes
planar under certain regularity conditions. The key ideas are to use the
Cole-Hopf transformation and to apply the Poincar\'{e} inequality to handle
with the two dimensional structure.
