This paper explores the nonlinear static response of bio-inspired helicoidal laminated composite (BiHLC) plates supported by a Pasternak medium. A combined analytical framework is established by integrating the mixed interpolation of tensorial components (MITC3i) approach with the first order shear deformation plate theory (FSDT). The Pasternak foundation is characterized by its spring stiffness k1 and shear stiffness k2. Based on the Lagrangian energy principle and von Kármán nonlinear theory, the governing equations are formulated and numerically solved through the Newton–Raphson iterative procedure. The effectiveness of the novel method is verified through comparisons with published documents. Additionally, the effects of helicoidal stacking sequences, geometric configurations, boundary constraints, and foundation rigidity on the large deflection behavior are analyzed. An artificial neural network (ANN) model is also proposed to estimate displacements efficiently, eliminating the dependence on finite element computations.