Molecular velocity distribution functions have been measured throughout a normal,M = 1.59helium shock wave that was formed in a low‐density wind tunnel. The measurements were obtained by using the electron beam fluorescence technique. Throughout the shock transition, distributions of random velocities were observed from directions both parallel and perpendicular to the flow. Also, direct measurements were made of the density and the flow velocity. The shock wave satisfied the continuity, momentum, and energy equations within the accuracy of the measurements. Parallel and perpendicular temperatures compare favorably to predictions derived from the Navier‐Stokes equations. In the upstream portion of the shock the distributions of parallel peculiar molecular velocities predicted according to the Chapman‐Enskog first iterate differ significantly from the experimental results, although as mentioned the second moments or temperatures agree with the Navier‐Stokes values.