Yield points have been detected in both GaAs and Fe-3wt%Si single crystals when contacting the surface with sharp diamond tips. The present study concentrates mostly on Fe-3wt%Si and demonstrates that a unique point in the load-displacement curve can be associated with the first dislocation nucleated. This occurs at loads in the vicinity of 100 μN for a 66 nm radius tip. Subsequently, this produces an avalanche of dislocations estimated to range from about 15 to 74 in number depending on the magnitude of the yield point load. A model, based upon discretized dislocations is proposed for both the initiation of yielding at an upper yield point (UYP) and the arrest of the indenter at a lower yield point (LYP). The UYP is interpreted in terms of Rice's unstable stacking energy concept, previously applied to crack tips, and accounts for tip radius, oxide film thickness and image force effects. The LYP is interpreted in terms of the back forces provided by previously emitted shielding dislocations. These two approaches provide first order solutions of the upper and lower yield points which both vary from test to test by as much as a factor of four. The large variation in nucleation load is proposed to be due to point to point differences in oxide thickness which might range from 4.5 to 8.5 nm.