Spherical indentations with deep penetration were conducted to single-crystal Cu along [001] direction. Zigzag slip bands induced by intersection of two groups of slip bands were found in the indentation pile-up region. On the material surface in the indentation pile-up region, micro-cracks were initiated along the slip bands radial to the indentation impression. The initiation of the micro-crack is affected by the indentation load and indenter radius. 3D crystal plasticity finite element simulation was applied to study the spherical indentation. Simulation results showed that the primary slip systems activated in indentation pile-up region were , whose slip planes make intersection lines tangent to indentation impression on the material surface. These two groups of slip bands, which both move outward the material surface, will intersect with each other and produce zigzag slip bands and jogs. The jogs would cause local stress concentration and thus provided the driving force to the initiation of micro-cracks. Meanwhile, simulation showed that the stress triaxiality in indentation pile-up region was around 0.6, which are closed to the stress state of plane strain tension and quite favorable to the initiation of cracks. Through simulations of spherical indentation along , it illustrated that the initiation of cracks may be orientation dependent.