A computational model for hydrogen transport, hydrogen induced deformation and fracture in metals that form binary hydrides, such as Zr and Ti alloys, is presented. The model uses a continuum description of the two-phase (metal + hydride) material, and solves the multi-field partial differential equations for temperature and stress-directed hydrogen diffusion together with mechanical equilibrium in a three-dimensional finite element setting. Point-kinetics models are used for metal-hydride phase transformation and stress-directed orientation of hydride precipitates, while a cohesive zone fracture model caters for initiation and propagation of cracks. The local fracture properties of the hydrided material are correlated to the calculated local concentration and orientation of the hydride precipitates, which have a strong embrittling effect on the material. In Part I of this two-part paper, we present sub-models applied for the aforementioned phenomena together with a detailed description of their numerical implementation. The applicability of the model is then demonstrated by simulating five independent experiments on hydrogen transport, metal-hydride phase transformation and stress-directed hydride orientation in zirconium alloys. Based on the results, we conclude that the model captures these phenomena over a wide range of thermo-mechanical loading conditions, including thermal cycling. Part II of the paper is focussed on fracture, and includes details on the fracture model and its validation against tests and experiments on initiation and propagation of hydride induced cracks.