Biological structures, such as mantis shrimp crustacean, provide a rich source of inspiration for constructing high-performance materials with an excellent mechanical strength and impact resistance. Therefore, helicoidal structures inspired by mantis shrimp were investigated to explore the static and dynamic properties. The first-order shear deformation theory of plates was used to describe the displacement field of laminated helicoidal composite plates. By the finite-element analysis (FEA), the bending and vibrations of bio-inspired composite plates were studied numerically using the ANSYS mechanical analysis software and the parametric design language APDL. Three classical orientations (unidirectional, cross-ply, and quasi-isotropic) and two helicoidal (linear and Fibonacci) orientations were considered. The “SHELL281” finite element of the APDL tool was exploited to solve the problem numerically with three integration points in each direction. The model proposed was verified, and its parametric studies were performed to clear up the effects of fiber orientation, slenderness ratio, and elasticity ratio on the static and free vibrations of a Bouligand composite plate. Results showed that the composite material had extraordinary mechanical properties, which is highly important for their unlimited applications in military industry and civil engineering