We compare new observations on the kinematic characteristics of the damped Ly alpha systems against results from numerical smoothed particle hydrodynamics (SPH) simulations to test the predictions of hierarchical galaxy formation. This exercise is particularly motivated by recent numerical results on the cross section of damped Ly alpha systems. Our analysis focuses on the velocity widths of Delta upsilon of approximate to 50 low- ion absorption profiles from our sample of z>1.5 damped Ly alpha systems. The results indicate that current numerical simulations fail to match the damped Ly alpha observations at high confidence levels ( 99.9%). Although we do not believe that our results present an insurmountable challenge to the paradigm of hierarchical cosmology, the damped Ly alpha observations suggest that current numerical SPH simulations overlook an integral aspect of galaxy formation.