A model of the effective low-strain elastic Young's modulus of multi-layer stacked composites is proposed, which is capable to account for an arbitrary stacked inclusion. Geometrical and discretization-based model results are validated against measured effective Young's moduli (from 10 up to 40 kPa) on 14 molded silicone specimens embedding a stiff (298 kPa) inclusion with variable size, position, and stacking. Specimens without inclusion represent the muscle, superficial, and epithelium layers in a human vocal fold with Young's moduli between 4 and 65 kPa. The proposed model allows to predict the influence of a stiff inclusion, mimicking a structural abnormality or pathology somewhere within the vocal fold, on the low-strain effective Young's modulus. Quantifying the influence of an inclusion or local stiffening on the vocal fold bio-mechanics is a necessary step toward the understanding and mitigation of structural vocal fold pathologies and associated voice disorders.