A new cellular automaton technique was developed based on the finite difference scheme to analyze structures such as beams and plates as well as the acoustic wave equation. The technique uses rules for a cell, and the rules are applied to all the cells repeatedly. The technique is very easy to write a computer code and computationally efficient. Like the standard cellular automaton, many different boundary conditions can be applied easily to the new technique. The technique was applied to both structural and fluid–structure interaction problems. The fluid domain was modeled as either the acoustic medium without flow using the newly developed cellular automaton rules or the fluid flow medium using the lattice Boltzmann technique. Multiple example problems were presented to demonstrate the new technique. Those included dynamic analyses of beams and plates, acoustic wave problems, and coupled fluid–structure interaction problems.