We study numerically the properties of a lattice model for the irreversible adsorption of proteins from solution onto a solid surface. The model is applicable to rigid proteins which undergo orientational changes on adsorption, e.g., fibrinogen or albumin. A protein is modeled as a rod of length I which can be adsorbed in two surface states, S-1 and S-2. In state S-1 the rod is normal to the surface and weakly bound, occupying 4 sites of the lattice, while in the more firmly bound state S-2 the surface parallel molecule occupies 4 + 2(l-1) sites. The surface exclusion effect is modeled by requiring that any site of the lattice may be occupied only once. No desorption is permitted from either state. The rod adsorbs initially in state 1 with probability lambda and in state 2 with probability 1 - p. At each time step all perpendicular rods attempt to tilt with probability lambda. We study the total theta(t;l;p,lambda) and partial theta(1)(t;l,p,lambda) and theta(t;l,p,lambda) coverages for different values of l, p, and lambda. In particular, lambda = 0 is equivalent to the adsorption of a mixture of squares and rods with no tilting. Short rods, l = 2, behave differently from longer rods when tilting is permitted in the model.