Perfusion chambers of rectangular cross section are often used for cell and tissue engineering purposes. In such chambers, growth medium flows in a laminar fashion over the cell bed located on the bottom of the chamber. The secretion of physiologically active protein from the cell bed is important in tissue function. Nonuniformity in the flow distribution near the side walls leads to concentration gradients of secreted protein. The magnitude of this concentration gradient is estimated for physiological protein secretion rates, for various aspect ratios and fluid flow rates using the finite element method. The thickness of hydrodynamic boundary layer extending from the side wall (delta(h)) is flow rate invariant, while the thickness of corresponding concentration boundary layer (delta(m)) decreases with increasing flow rate. The ratio of delta(m) to delta(h) always exceeds unity and varies with the flow-rate and aspect ratio. Thus, an extended concentration gradient can emanate from the side wall of the chamber even for high aspect ratios. The estimation of the magnitude of this concentration gradient shows that it can be large enough to cause chemotactic cell motion toward the side walls. This chemotactic motion in turn can lead to nonuniform cell growth and be a detriment to effective reconstitution of tissue function ex vivo.