The paper is devoted to the development of ray diffraction theory for arbitrary nonconvex smooth obstacles both for the scalar and elastic case. The consideration is restricted to two‐dimensional problems. An exact expression for the ray amplitude with an arbitrary number of reflections is derived from repeated Kirchhoff integrals using the stationary phase method. It is shown that the difference between scalar and elastic cases consists of the reflection coefficients that are present for the second case. Some examples are considered as a demonstration of the theory.