In the present study, acoustic characteristics of fractal structures are modeled and studied using Cellular Automata (CA). CA is a discrete system which consists of finite state variables arranged on uniform grid (cell). The dynamics of CA is expressed by temporary updating the states of cells according to the local interaction rules, defined among a cell and its neighbors. In this paper, the influence of the fractal shaped structures to the property of wave propagation phenomena in free field is investigated. Local rules are provided for the construction of three-dimensional fractal structures as well as representation of wave propagation phenomena.