This thesis presents and discusses hydrogen diffusion modelling as a first step in predicting and mitigating hydrogen-assisted fracture. Hydrogen embrittlement is a common phenomenon that degrades metals and alloys, and related failures are usual in industry.However, the relationship between hydrogen and the transition from ductile to brittle modes of fracture is not entirely clear. Even though mechanism operating at nano and microscalesare not yet completely understood, it has been proved that embrittlement is proportional to hydrogen concentration within a metal. Therefore, the present work has the objective of establishing, validating, implementing and analysing a consistent numerical model for hydrogen diffusion, in a Continuum Mechanics framework by means of a Finite Element software.Diffusion phenomena are reviewed and particularised on hydrogen transport in metals. In particular, a "two-level" model, considering trapping effects explicitly, is chosen in order to simulate hydrogen diffusion near a crack tip. Strain and stress fields present in a crack or notch are connected with hydrogen diffusion; additionally, hydrogen promotes a local softening, a dilatation and a reduction in cohesive energy so a coupled behaviour between diffusion, elasto-plasticity and damage must be considered.Finally, numerical models for diffusion are applied to fracture modelling in a Cohesive Zone Model approach and a notched tensile test is simulated, demonstrating that the combination of diffusion with damage models might predict brittle fracture. Vessels storing hydrogen are also simulated with the purpose of finding hydrogen distributions near stress concentrators; influence of cyclic loads and compressive residual stresses is also evaluated in these deposits.