Classical Irregular Scattering and Fluctuation of Quantum Transition Probability Seiji Takahashi and Kiyohiko Someda Department of Basic Sciences, Graduate School of Arts and Sciences, The University of Tokyo S-matrix of the system exhibiting classical irregular scattering is analyzed on the basis of the classical S-matrix theory. The S-matrix is represented as an infinite series each term of which possesses a random phase factor. The S-matrix element, in consequence, performs random walk on the complex plane when one varies the final state. Probability distribution of the S-matrix element is derived theoretically.