Low Reynolds number flow of liquids over micron-sized structures and the control of subsequently induced shear stress are critical for the performance and functionality of many different microfluidic platforms that are extensively used in present day lab-on-a-chip (LOC) domains. However, the role of geometric form in systematically altering surface shear on these microstructures remains poorly understood. In this study, 36 microstructures of diverse geometry were chosen, and the resultant overall and facet shear stresses were systematically characterized as a function of Reynolds number to provide a theoretical basis to design microstructures for a wide array of applications. Through a set of detailed numerical calculations over a broad parametric space, it was found that the top facet (with respect to incident flow) of the noncylindrical microstructures experiences the largest surface shear stress. By systematically studying the variation of the physical dimensions of the microstructures and the angle of incident flow, a comprehensive regime map was developed for low to high surface shear structures and compared against the widely studied right circular cylinder in cross flow.