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Pressure-driven flows in pipes and channels are known to be vulnerable to a certain type of instability―the so-called hydroelastic instability. This type of instability is encountered when the channel is made of compliant materials. In practice, modes which are normally stable in a rigid channel are then seen to become unstable in such deformable channels. Interestingly, the instability is found to exhibit itself also under creeping condition even for Newtonian fluids. This finding is of potential importance for mixing enhancement in microfluidic devices. That is, because of the Reynolds number being vanishingly small in such devices, they suffer from a poor mixing due to the laminar nature of creeping flows. There are different passive and active means to improve mixing at such small-scale devices. Obviously, one cannot usually rely on mechanical means such as stirrers for this purpose. An interesting idea is to cover the inner surfaces of the channel with a thin or thick layer of a soft polymeric gel. As soon as the fluid flow is established, certain waves may then become unstable at the fluid/solid interface, no matter how small the Reynolds number is. Such waves eventually lead to turbulence causing a huge improvement in the level of heat and mass transfer, whenever needed. Based on current knowledge, the rheological properties of the solid gel is known to play a key role for the success of this operation. The same is known to be true as to the rheological properties of the working fluid. A variety of solid and fluid models have been used in previous studies when tackling this formidable fluid/solid interaction (FSI) problem. As to the fluid side, most studies carried out in the past has assumed that the fluid is Newtonian. This is irrespective of the fact that, physiological fluids tested in microfluidic devices are often realized be non-Newtonian. In a recent work, the effect of a fluid’s viscous behavior has been investigated on the hydroelastic instability in creeping planar Poiseuille flow using the power-law model. But, the effect of a fluid’s yield stress on this type of instability still remains unexplored. In the present work, we intend to investigate the role played by a fluid’s yield stress on the hydroelastic instability in plane channel flow. For the results to be more representative of the real world , we allow the polymeric Hydroelastic Instability of Viscoplastic Fluids in Plane Channel Flow