Summary: This paper presents a shortest path search algorithm using a model of excitable reaction-diffusion dynamics. In our previous work, we have proposed a framework of Digital Reaction-Diffusion System (DRDS)--a model of a discrete-time discrete-space reaction-diffusion system useful for nonlinear signal processing tasks. In this paper, we design a special DRDS, called an "excitable DRDS," which emulates excitable reaction-diffusion dynamics and produces traveling waves. We also demonstrate an application of the excitable DRDS to the shortest path search problem defined on two-dimensional (2-D) space with arbitrary boundary conditions.