Zirconium cladding materials undergo hydride-related degradation during the dry storage of spent nuclear fuel. We investigated the effects of not only internal stress due to the lattice mismatch between α-Zr and δ-hydride but also applied stress to the hydride morphology using the Multiphysics Object Oriented Simulation Environment (MOOSE) framework. We introduced the CALPHAD-based Gibbs free energies of the α-Zr-H and δ Zr-H solid solutions. To enhance the numerical stability of the calculation, these free energies were approximated using quadratic polynomials near the equilibrium composition. Using the finite element method-based phase-field kernel and the tensor-mechanics kernel in the MOOSE framework, we simulated the microstructural change in the hydride in the presence of internal and external stresses. We assumed a cladding temperature of T= 550 K, which is a typical cladding temperature during the dry storage process. Initially, the spherical δ-hydride nuclei were located at the centers of the 3D α-Zr matrix simulation cells and then we simulated the morphological evolution of the zirconium hydride. With our developed phase-field model, which considers elasticity, we successfully captured the morphological evolution from the initial spherical nuclei to the platelet hydride. As the stress level applied to the system increased, the hydride rotated more however, the hydride did not rotate further once the applied stress level was above a certain value. In addition, we qualitatively measured how the magnitude of the applied stress affected the shape evolution of the hydride.