Since modern design and analysis use complex numerical simulations, they require advanced knowledge of material properties. Heterogeneity plays a significant role in modeling natural materials, such as soft tissues, and anthropogenic materials, including concrete and composites. In this study, the Finite Element Model Updating methodology, previously employed in nonlinear thin shells to reconstruct spatial fields of properties, such as constitutive parameters [1], mass density [2], or prestrain [3], is generalized to thin shells subjected to mechanical contact. Nonlinear thin shells — the forward problem — utilize a direct surface formulation, which is further discretized using a rotation-free isogeometric (IGA) Finite Element Method [4]. The reconstructed fields are discretized with low-order (constant or bilinear) Lagrange elements, referred to as the material mesh [1]. Thus, the nodal values of the material mesh become the unknowns of the inverse problem. The inverse problem is a PDE-constrained optimization task, where the minimized objective function is a least squares error between numerical and experimental full-field displacements. If the displacements cannot solely determine the inverse problem, other quantities, such as contact forces, enter the objective function. The objective function is minimized using the Trust-Region Interior Reflective approach from MATLAB lsqnonlin solver — a gradient-based optimization algorithm — providing analytical objective function derivatives. The proposed inverse approach is verified with numerical examples, including 2D ironing and 3D abdominal wall indentation, utilizing synthetic experimental data affected by noise. The results show that mechanical contact can generate full-field data with high information content, which can be successfully used for property inversion, given an appropriate IGA and material meshes. The proposed contact-based inverse analysis framework is able to accurately reconstruct spatial distributions of properties for isotropic constitutive shell models, such as Koiter, Neo-Hooke, and Canham shell models.