In the present work, a coupled system of phase field and elasticity equations is solved to simulate phase transformations (PTs) for a single martensitic variant under thermal and mechanical loadings in the Cartesian coordinate system. The linear finite element method (FEM) is used to solve the linear (small strain based) elasticity equations for a plane stress problem. On the other hand, the nonlinear time-dependent phase field (Ginzburg-Landau) equations in 2D are solved using the nonlinear finite element method. Next, the elasticity and phase field equations are coupled and solved using the FEM method and the developed code. The system of equations and the numerical procedure are verified using existing analytical solutions. Linear triangle elements and explicit method have been used in the FEM code. The stability and the mesh and time step independence of the solutions have been discussed. For the phase field equation, the isolated boundary condition is considered everywhere, imposing the constant surface energy over the simulation domain. Examples of cubic to tetragonal phase transformations in 2D for a single martensitic variant are presented including plane interface propagation, martensitic nucleus growth and reverse phase transformation under thermal and different mechanical loadings. The austenite- martensite interface velocity, width and energy have been obtained. The threshold stresses for austenite to martensite PTs for the uniaxial and biaxial loaidngs and reverse PTs are calculated. It is found the results are in a good agreement with the transformation work based criterion. The developed FEM code represents a proper and accurate tool to study the PTs including nucleation, growth and propagation of transformed phase, reverse PTs and equilibrium and stability conditions for phase transformations under mechanical and thermal loadings in 2D. A further development of the numerical procedure provides a powerful tool for the study of more complicated PTs. Keywords: Martensitic phase transformation; Phase field approach; Finite element method; Nanoscale