Martensitic phase transformation (PT) is a first-order, displacive and diffusionless PT which plays an important role in the formation of nano and microstructures and mechanical properties in many materials such as smart alloys. In this project, the coupled system of phase field and large strain based elasticity equations is solved using the nonlinear finite element method (NFEM) to simulate the single-variant direct and reverse martensitic PT at the nanoscale under different mechanical and thermal loadings in 2D and in the Cartesian coordinate. First, the NFEM was used to solve the time dependent phase field or Ginzburg-Landau (GL) equation without mechanics and the numerical procedure and the self-developed code were verified using the existing analytical solutions. Next, the large strain based stationary elasticity equations were solved using the NFEM and the developed code was verified. Finally, the GL and the large strain based elasticity equations were coupled through the elastic energy and the transformation strain tensor and were solved using the NFEM based on both the explicit and implicit methods and both the total and updated Lagrangean descriptions. Several examples of the cubic to tetragonal PTs in NiAl were simulated consisting of the creation and propagation of a planar A-M interface, growth of martensitic nucleus, nanostructure evolution and reverse PT induced by thermal and mechanical loadings and their combination. The developed code gives the ability to study various phenomena similar to martensitic phase transformations such as reconstructive PTs, diffusion and so on. Keywords: Nonlinear finite element, Large strains, Nanoscale, Phase field, Martensitic phase transformation