Fibrinogen, a blood glycoprotein of vertebrates, plays an essential role in blood clotting by polymerizing into fibrin when activated. Upon adsorption on material surfaces, it also contributes to determine their biocompatibility and has been implicated in the onset of thrombosis and inflammation at medical implants. Here we present the first fully atomistic simulations of the initial stages of the adsorption process of fibrinogen on mica and graphite surfaces. The simulations reveal a weak adsorption on mica that allows frequent desorption and reorientation events. This adsorption is driven by electrostatic interactions between the protein and the silicate surface as well as the counterion layer. Preferred adsorption orientations for the globular regions of the protein are identified. The adsorption on graphite is found to be stronger with fewer reorientation and desorption events and shows the onset of denaturation of the protein.