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Zirconium-based alloys are common materials for light water reactor (LWR) fuel cladding. These alloys readily absorb hydrogen and are subjected to lose ductility due to hydride accumulation. A phase-field modeling code with Calphad-based free energy functions, Hyrax, has been used to model the hydrogen solvus in α -zirconium solution and the formation of the δ zirconium-hydride phase in the α -zirconium matrix. The modeled hydrogen solvus was compared against published experimental data; this is considered the first direct validation of Hyrax output. The effect of external stress on hydrogen solvus and hydride formation has also been modeled. A tensile stress was uniformly applied to a single zirconium crystal and a bi-crystal system. We observed that the stress does not affect hydrogen solvus but does cause hydride to accumulate in the crystalline which has the c-axis parallel to the stress direction. This is because the external stress creates a strain energy gradient across the system; the δ -hydride preferentially precipitates in the low strain energy region which yields more lattice misfit strain to compensate the gradient.