Ongoing investigations are exploring the biomechanical properties of isolated and suspended biological cells in pursuit of understanding single-cell mechanobiology. An optical tweezer with minimal applied laser power has positioned biologic cells at the geometric center of a microfluidic cross-junction, creating a novel optohydrodynamic trap. The resulting fluid flow environment facilitates unique multiaxial loading of single cells with site-specific normal and shear stresses resulting in a physical albeit extensional state. A recent two-dimensional analysis has explored the cytoskeletal strain response due to these fluid-induced stresses [Wilson and Kohles, 2010, “Two-Dimensional Modeling of Nanomechanical Stresses-Strains in Healthy and Diseased Single-Cells During Microfluidic Manipulation,” J Nanotechnol Eng Med, 1(2), p. 021005]. Results described a microfluidic environment having controlled nanometer and piconewton resolution. In this present study, computational fluid dynamics combined with multiphysics modeling has further characterized the applied fluid stress environment and the solid cellular strain response in three dimensions to accompany experimental cell stimulation. A volumetric stress-strain analysis was applied to representative living cell biomechanical data. The presented normal and shear stress surface maps will guide future microfluidic experiments as well as provide a framework for characterizing cytoskeletal structure influencing the stress to strain response.