Direct numerical simulations (DNS) are carried out to investigate the kinematics of vortical structures in a ho-mogeneous shear flow. Generated longitudinal (streamwise) vortices are conditionally averaged over all the computational region. The effects of the non-linear term on their kinematics are investigated by comparing the DNS and Rapid Distortion Theory (RDT) in both high and low Reynolds number flow fields. It is found that the strain rates in the vortical structure are generated by the effects of the non-linear term and closely associated with the kinematics of the vortical structure. As the Reynolds number increases, the wrapping of the streamwise velocity fluctuation around the vortex is more enhanced to augment the strain rate inside the vortex.