Nanoindentation is a widely used technique for characterizing the mechanical properties of materials at the nanoscale by applying controlled force through a sharp indenter and measuring the resulting material deformation. However, it is challenging to access the complex stress states during elastic-plastic deformations occurring beneath the indenter, which are crucial to bridge the microscopic plastic deformation carriers, dislocations and their slip systems, to the macroscopic mechanical behavior of the material. To address this, finite element simulation of nanoindentation is essential. Conventional mate-rial models in finite element software, such as ANSYS, are typically developed for bulk materials and are unable to accurately describe the microscopic plastic behaviors, such as the activation of slip systems in crystalline structures. Crystal plasticity finite element methods (CPFEM), which incorporate slip systems, are currently available only in the ABAQUS CAE finite element software. To further improve efficiency and flexibility of CPFEM, a custom user-defined material subroutine within the ANSYS Parametric Design Language (APDL) platform was developed in this thesis. This method accounts for both elastic and plastic crystal deformation, as well as the crystal plasticity constitutive laws specific to the deformation behaviour of the hexagonal close-packed structure of magnesium. In this subroutine, the elastic component of the material model was validated against experimental elastic modulus values from the literature, accounting for various crystallographic orientations. The plastic component was validated using Kelley-Hosford plane strain compression test data and compared with the simulation results of Graff et al. The material model was then integrated with the nanoindentation loading conditions, to determine the complex stress states in each element and the load-displacement curves for single-crystal magnesium along c-axis, a-axis, and six other grain orientations. Finally, the activity of basal, prismatic, and pyramidal <c+a> slip systems was analyzed for each orientation. This work provides an open-source material subroutine designed to predict the crystallographic dependent mechanical behavior of magnesium. By clarifying the details of microscopic plastic deformation, this tool provides valuable insights for designing advanced magnesium for applications in the aerospace, automotive, and biomedical fields.