In vitro systems for applying mechanical strain to cultured cells are commonly used to investigate cellular mechanotransduction pathways in a variety of cell types. These systems often apply mechanical forces to a flexible membrane on which cells are cultured. A consequence of the motion of the membrane in these systems is the generation of flow and the unintended application of shear stress to the cells. We recently described a flexible system for applying mechanical strain to cultured cells, which uses a linear motor to drive a piston array to create biaxial strain within multiwell culture plates. To better understand the fluidic stresses generated by this system and other systems of this type, we created a computational fluid dynamics model to simulate the flow during the mechanical loading cycle. Alterations in the frequency or maximal strain magnitude led to a linear increase in the average fluid velocity within the well and a nonlinear increase in the shear stress at the culture surface over the ranges tested (0.5–2.0 Hz and 1–10% maximal strain). For all cases, the applied shear stresses were relatively low and on the order of millipascal with a dynamic waveform having a primary and secondary peak in the shear stress over a single mechanical strain cycle. These findings should be considered when interpreting experimental results using these devices, particularly in the case when the cell type used is sensitive to low magnitude, oscillatory shear stresses.