A model is used to study the viscous wall region of turbulent shear flows over rigid flat surfaces. Periodic boundary conditions are imposed in the horizontal directions with periodicity lengths that are several times larger than the experimental streak spacing. In order to sustain the turbulence in the viscous wall region, the averagedxcomponent of the velocity is set equal to a fixed profile outside the viscous wall region. Pseudospectral methods are used to solve the governing equations with the Marcus time splitting scheme. It is shown that a model of the viscous wall region can reproduce much of the behavior seen in direct simulations of turbulence that place greater demands on computer resources. The model is used to investigate the flow of energy in the viscous wall region and the relationship between low‐speed streaks and vortices in the viscous wall region.