The scattering problem on the Bruhat-Tits tree being the realization o
f the p-adic hyperbolic plane is studied. The spectral decomposition o
f the corresponding Laplace-Beltrami operator is constructed. The Lax-
Philips resonance scattering theory for the problem is developed in a
closed form. The properties of the analytic continuation of the S-matr
ix are described.