An adaptive meshing procedure is developed for the analysis of thin shell structures that experience localized elastic deformations associated with the formation of folds. The refinement criterion for remeshing takes into consideration the localization of deformation in the folds, while avoiding excessive refinement outside this region. The local bending strains in two principal directions are used to construct the refinement criterion. A geometrical parameter related to a boundary layer effect is shown to be effective as a limit length for refinement. Isogeometric shell finite elements are used for the simulations. Different tape spring geometries are simulated to illustrate the generality and efficiency of the proposed adaptive procedure.