One of the key issues associated with the utilization of block copolymer (BCP) thin films in nanoscience and nanotechnology is control of their alignment and orientation over macroscopic dimensions. We have recently reported a method, solvent vapor annealing with soft shear (SVA-SS), for fabricating unidirectional alignment of cylindrical nanostructures. This method is a simple extension of the common SVA process by adhering a flat, crosslinked poly(dimethylsiloxane) (PDMS) pad to the BCP thin film. The impact of processing parameters, including annealing time, solvent removal rate and the physical properties of the PDMS pad, on the quality of alignment quantified by the Herman's orientational factor (S) is systematically examined for a model system of polystyrene-block-polyisoprene-block-polystyrene (SIS). As annealing time increases, the SIS morphology transitions from isotropic rods to highly aligned cylinders. Decreasing the rate of solvent removal, which impacts the shear rate imposed by the contraction of the PDMS, improves the orientation factor of the cylindrical domains; this suggests the nanostructure alignment is primarily induced by contraction of PDMS during solvent removal. Moreover, the physical properties of the PDMS controlled by the crosslink density impact the orientation factor by tuning its swelling extent during SVA-SS and elastic modulus. Decreasing the PDMS crosslink density increases S; this effect appears to be primarily driven by the changes in the solubility of the SVA-SS solvent in the PDMS. With this understanding of the critical processing parameters, SVA-SS has been successfully applied to align a wide variety of BCPs including polystyrene-block-polybutadiene-block-polystyrene (SBS), polystyrene-block-poly(N,N-dimethyl-n-octadecylammonium p-styrenesulfonate) (PS-b-PSS-DMODA), polystyrene-block-polydimethylsiloxane (PS-b-PDMS) and polystyrene-block-poly(2-vinlypyridine) (PS-b-P2VP). These results suggest that SVA-SS is a generalizable method for the alignment of BCP thin films.