The mechanical properties of metallic systems at the nanoscale can be modified by varying their structure and composition. One example of a deformation-resistant structure is a core-shell nanostructure (CSN). In the present work, we use molecular dynamics simulations to perform nanoindentation and retractions to understand plastic deformation of core-shell nanostructures. The core consists of aluminum (Al), the shell is amorphous silicon (a-Si), and the substrate is either crystalline Al or a-Si. The unique aspect of this work is that we study the deformation behavior of CSNs that contain symmetric and asymmetric grain boundaries in the core with two different orientations; comparisons are made to deformation in a CSN with a single-crystal core. Nanoindentation on CSNs with 5 nm and 10 nm core radii shows that the elastic stiffness with and without a grain boundary is similar when the substrate material is the same. Five-nanometer-core-radius CSNs with a-Si and Al substrates and an asymmetric tilt grain boundary in the core show 100% recovery from dislocation plasticity, but damage within the core leads to reduction of similar to 50% of the atoms that no longer being identified as FCC crystal structure, which makes these CSNs non-deformation-resistant. CSNs with Al substrate (5 nm and 10 nm core radii) obtained 100% recovery from plasticity and retained its crystal structure after unloading when the core is single crystal or contains a symmetric tilt grain boundary. Moreover, a single-crystal core can withstand nanoindentation to 100% of the shell thickness, whereas a symmetric tilt grain boundary core can only withstand nanoindentation about 80% of the shell thickness and still have 100% recovery from plasticity. Therefore, CSNs with single-crystal core are more reliable for deformation-resistant behavior than those that contain grain boundaries.