In order to consider the modified Lax-Phillips conjecture for scattering by obstacles consisting of several convex bodies, the zeta functions of a dynamical system in the exterior of the obstacle play an important role. In this paper we develope a theory for singular perturbations of symbolic dynamics and consider the zeta functions associated with dynamical systems. We give a sufficient condition for the existence of poles of the zeta functions of the singularity perturbed dynamics. As the application of this theory, the validity of the modified Lax-Philipps conjecture for obstacles consisting of small balls is proved.