This thesis primarily explores the stability of spherically capped conical shells and secondarily explores the nature of the polygonal folds observed during these deformations. The polygonal folds were classified according to the number of facets observed. The problem is primarily explored using Finite Element Method (FEM) studies of rigid indentations of spherically capped conical shells of varying thickness, cone angle, and slant height. The main finding of the FEM studies is that the capped shells suddenly buckle during the indentation as the ridge approaches the region where the cap and conical shell meet. The geometry of this join region dominates the shell response for all the studied spherically capped conical shells and provides another perspective on how local geometry affects a shell’s response to indentation. Experimentally a commercially bought rubber conical shell is qualitatively observed to show that the shell can be poked and folded to remain statically in a wide number of folded shapes. While the thesis does not answer the reason for this stability, the combination of the FEM studies and exploration of the rubber conical shell suggest that the observed stability is likely linked to the interaction between the cap and conical shell.