Pulsatile flow of thixotropic fluids is investigated numerically in a partially-constricted tube assuming that the fluid obeys Moore's structural model as is constitutive equation. Assuming that the flow is laminar, incompressible, two-dimensional and axisymmetric, the equations of motion are simplified using lubrication theory. The simplified equations are then solved numerically using the finite difference method. A suitable coordinate transformation is used to immobilize the boundary of the tube. The effect of the structure breakdown/reformation parameters is investigated on the velocity field and wall shear stress distribution. The importance of the geometrical parameters of the constriction is also investigated on the flow characteristics.