Menger sponge has tunable electrical and mechanical properties with the hierarchical structure, which makes this structure more favourable for various applications, particularly for lightweight aerospace structures. In this paper Menger sponge-based photostrictive composite actuator is proposed. It consists of piezoceramic Menger sponge fractal shapes with square cavity-based fibres of different orders embedded in a soft polymer-based matrix. A numerical study has been carried out to investigate various orders (0th, 1st, 2nd, and 3rd) of such hierarchical structures with square-shaped cavities to determine their effective properties. The finite element method has been considered for a unit cell. The formulation of boundary conditions has been emphasized. The average volume method has been considered, which enables the simulation of all modes of overall deformation resulting from arbitrary combinations of electrical and mechanical loading. This numerical method provides a potential tool for rapidly calculating their effective properties. The results derived from the numerical approach are juxtaposed against results acquired through the analytical technique across various orders of the Menger sponge.