A numerical investigation of elasto-viscoplastic thixotropic liquids flowing past a cylinder confined in a parallel-plate channel is performed, using a recently proposed constitutive equation. The conservation equations are solved using a four-field Galerkin least-squares formulation in terms of the extra-stress, pressure, velocity, and structure parameter - a scalar quantity that represents the structuring level of the material microstructure. The focus is on determining the effect of both thixotropy and elasticity on the topology of yielded and unyielded regions of the channel. The effect on the cylinder drag coefficient is also studied. Relevant ranges of the dimensionless relaxation time and equilibrium time of the material structure are investigated. The numerical results reveal striking effects of thixotropy and elasticity. The trends observed are physically sound and in accordance with the related literature. (C) 2012 Elsevier B.V. All rights reserved.