Stability of purely-viscous fluids is numerically investigated in plane Poiseuille flow under the assumption that the channel's inner walls are coated with a purely-elastic compliant polymeric gel. Using the power-law model for representing the shear-dependent viscosity of the fluid and the neo-Hookean model for representing the elasticity of the gel, the basic flow/deformation for the fluid/solid are obtained numerically at vanishingly-small Reynolds numbers. The stability of the basic solution so-obtained is investigated when subjected to infinitesimally-small normal-mode perturbations. Using the linear temporal stability analysis, an eigenvalue problem is obtained which is solved numerically to determine the growth rate as a function of the fluid's rheology as represented by the power-law index. Based on the numerical results obtained in this work, it is concluded that at moderate power-law indices, the shear-thinning behavior of the working fluid has a stabilizing effect on the flow regardless of the thickness of the compliant layer. But, at power-law indices lower than a critical value (which depends on the layer thickness) numerical results suggest that shear-thinning can also destabilize the flow. (C) 2014 Elsevier B.V. All rights reserved.