Application of shear stress at the surface of a block copolymer thin film has been shown to substantially orient the microdomains in the direction of the applied shear. The present work systematically examines the influence of key material, film, and process parameters on this alignment behavior using a series of cylinder-forming polystyrene poly(n-hexyl methacrylate) copolymers. A parallel plate rheometer applies a radially dependent stress gradient to the film's surface through a viscous nonsolvent overlayer. The degree of alignment is assessed using atomic force microscopy and examined as a function of the applied stress. To quantitatively compare the alignment process across different block copolymer films, a melting recrystallization model is fit to the data, which allows for the determination of two key alignment parameters: the critical stress needed for alignment and an orientation rate constant. For films containing a monolayer of cylindrical domains, as polystyrene weight fraction or overall molecular weight increases, the critical stress increases moderately, while the rate of alignment drastically decreases. As the number of layers of cylinders in the film increases, the critical stress decreases modestly, while the rate remains unchanged. Substrate wetting condition has no measurable influence on alignment response over the range of conditions investigated. Collectively, these results provide useful quantitative rules that enable predictions of the level of alignment which will occur under particular shearing conditions.