An analytical study of the anisotropic velocity correlation spectrum tensor in the inertial subrange of homogeneous turbulent shear flow is performed using a Lagrangian renormalized spectral closure approximation. The analysis shows that the spectrum in the asymptotic limit of infinitely large Reynolds numbers Re is determined by two nondimensional universal constants; theoretical estimates for the constants are provided. The anisotropic component of the spectrum at finite Re is more sensitive to large-scale turbulence structures than the isotropic component. A preliminary analysis of the effect of finite Re or the width of the inertial subrange is in qualitative agreement with direct numerical simulations. (C) 2003 American Institute of Physics.