The structure of the small scale velocity field is studied in an approximately homogeneous shear flow (constant mean shear) over the Reynolds number range156⩽R&lgr;⩽390.The shear was generated in a wind tunnel using screens of various solidity and a series of straightening channels in the manner of Tavoularis and Corrsin [J. Fluid Mech.104, 311 (1981)]. We show there is significant skewness (of order 1) of the derivative of the longitudinal velocity in the direction of the mean gradient, and thus that for these Reynolds numbers the flow is anisotropic at the small scales. The skewness slowly decreases withR&lgr;and is described by the empirical fit:S∂u/∂y=15.4R&lgr;−0.6.Thus, even if this downward trend continues, our results imply that anisotropy at the third moment continues to very highR&lgr;.We also show that, over theR&lgr;range investigated, the kurtosis of∂u/∂ydecreases (due to the diminishing effect of the structures that cause the skewness), implying that there will be a transition in this quantity, since it must increase as intermittency becomes more pronounced at higherR&lgr;.Transverse (as well as longitudinal) structure functions of the longitudinal velocity are studied up to the fifth moment. It is shown that the third order transverse structure function has a scaling range. Thus, the anisotropy exists at inertial as well as dissipation scales. The results are compared and contrasted with those of a passive scalar (for which it is known that persistent anisotropy exists at the third moment and above). ©1998 American Institute of Physics.