Peristaltic pumping of thixotropic fluids is studied numerically in a flexible tube assuming that the fluid of interest is thixotropic and obeys Moore's rheological model. Assuming the flow to be laminar, axisymmetric and incompressible, the equations of motion are simplified using the long-wavelength approximation. It is shown that at high Reynolds numbers, the axial pressure gradient has the same functional form as the peristaltic wave with an amplitude which decays as the Reynolds number is increased. Using finite difference method (FDM) to solve the equations of motion, it is concluded that the peristaltic pumping of thixotropic fluids is governed by the ratio of the breakdown to the buildup parameters only, not their separate absolute values. An increase in the viscosity ratio (i.e., the ratio of zero-shear to infinite-shear viscosities) is found to decrease the axial velocity with no significant effect on the wall shear stress. But, an increase in the speed of the peristaltic wave is predicted to increase both the axial velocity and also the maximum wall shear stress.