Mechanical computing systems have historically faced challenges in efficiently integrating computation and memory functions, often leading to complex designs and limited scalability in applications ranging from micro-electromechanical systems (MEMS) to programmable matter. This study aims to address this issue by introducing a mechanical system based on cellular automata (CA) principles, utilizing a bi-threshold tristable mechanism for implementing nonlinear Boolean functions. The system’s design translates Elementary Cellular Automata (ECA) rules, such as Rule 110, into mechanical motion using compliant multistable mechanisms. Finite Element Analysis (FEA) and pseudo-rigid body simulations validate the operational feasibility of this approach. The results confirm the system’s capability to process complex computational tasks by mechanically embodying specific ECA rules. This development marks a step forward in mechanical computing, offering a more integrated approach to computational material design. The research establishes a methodical design approach, enabling the embodiment of a wide range of Elementary Cellular Automata (ECA) rules within the mechanical framework. This approach extends beyond linearly separable Boolean functions, illustrating a significant advancement in mechanical computing capabilities. The findings provide a basis for future work in scaling the system and exploring its applicability in fields such as programmable matter and intelligent mechanical systems.