Three-dimensional Finite Element simulations of mode I crack tip fields in Compact Tension specimens are presented for elastic ideally-plastic F.C.C. single crystals. The computations are carried out within the framework of classical continuum crystal plasticity for three crack orientations: (001)110,(110)001 and (001)100. The attention is drawn on the strong differences between the plastic strain field obtained at the free surface and in the mid-section of the specimens. The results are compared, on the one hand, to analytical solutions for stationary cracks in single crystals under plane strain conditions and, on the other hand, to experimental tests on a single crystal nickel-based superalloy at room temperature. For this material, both octahedral and cube slip must be taken into account. A good agreement between experimental observations and numerical results is found in the structure of the strain localization bands observed at the free surface of (110)001 cracked specimens. In particular, the evidence of kink banding near the crack tip is provided, confirmed by EBSD orientation mapping. The measured values of local lattice rotation are in agreement with the Finite Element prediction.