Recent experiments indicate that the first yield point of micron-sized metals exhibits significant statistical scatter as well as strong dependence on the specimen size. In this work, molecular dynamics (MD) simulations are carried out to investigate the onset of shear deformation in a small block of material, using an embedded atom potential for the intermetallic Ni3Al alloy. Incipient plasticity in the form of homogeneous dislocation generation is observed to occur at atomic sites with interatomic displacements approaching one-half of the Shockley partial Burgers vector. From the distribution function of the interatomic displacements observed in the MD simulations, the probability of a general material volume surviving under given loading conditions is predicted. The survival probability is then calculated for several situations, including homogeneous deformation and nanoindentation, to predict the critical load for incipient plasticity to occur in these situations. The predicted results are compared to micro-pillar compression and nanoindentation experiments on Ni3Al available in the literature.