Precipitation of ζ, γ, and δ hydride phases in nuclear fuel claddings is studied by developing a multi-phase field model. Non-conservative structural field variables are used to represent each phase including α-Zr matrix, ζ-hydrides, γ-hydrides (one structural field variable for each of the three orientation variants), and δ-hydrides. Concentration of Hydrogen is controlled using a conserved field variable. The Ginzburg-Landau and Cahn-Hilliard equations are used for the evolution of field variables and concentration, respectively, and the mechanical equilibrium equations are imposed to consider the effects of elastic strain energy. Results from simulations both in the basal plane and perpendicular to the basal plane with and without applied stresses indicate that the initial morphology of δ hydrides is significantly dependent on the intermediate phases. Simulations conducted including only α and δ phases showed significantly different results from simulations including the intermediate phases.