First-principles density-functional theory has been used to investigate equilibrium geometries, total energies, and diffusion barrfiers for H as an interstitial impurity absorbed in bcc-Fe. Internal strains/stresses upon hydrogen absorption are a crucial factor to understand preferred absorption sites and diffusion. For high concentrations, H absorbs near the octahedral site favouring a large tetragonal distortion of the bcc lattice. For low concentration, H absorbs near the tetrahedral site minimizing the elastic energy stored on nearby cells. Diffusion paths depend on the concentration too; hydrogen diffuses about ten times faster in the distorted bct lattice. External stresses of several GPa modify barriers by 10/100, and diffusion rates by 30/100.