For a cracked structural component the crack tip loading rate very often exceeds the maximum rate prescribed in current fracture toughness standards, e.g., ASTM E813. In a previous work, Lorentzon and Eriksson, it was found that loading rates at and just above the ASTM limit significantly affect the fracture toughness of ordinary structural steels. The effect of the loading rate upon the stress and strain distribution around a mode I plane strain crack tip has been calculated with the finite element method. A boundary layer formulation based upon Westergaard's exact analytical solution for an infinite plate and a Perzyna visco-plastic material model has been used. The results show that viscous effects are significant only very close to the crack tip.