This note is concerned with the application of Finite Element Methods (FEM) and Newton-Multigrid solvers for the simulation of thixotropic ow problems. The thixotropy phenomena are introduced into viscoplastic material by taking into ac-count the internal material micro structure using a scalar structure parameter. Firstly, the viscoplastic stress is modied to include the thixotropic stress dependent on the structure parameter. Secondly, an evolution equation for the structure parameter is introduced to induce the time-dependent process of competition between the destruction (breakdown) and the construction (buildup) inhabited in the material. Substantially, this is done sim-ply by introducing a structure-parameter-dependent viscosity into the rheological model for yield stress material. The modied thixotropic viscoplastic stress w.r.t. the structure parameter is integrated in quasi-Newtonian manner into the generalized Navier-Stokes equations and the evolution equation for the structure parameter constitutes the main core of full set of modeling equations, which are creditable as the privilege answer to incorporate thixotropy phenomena. A fully coupled monolithic nite element approach has been exercised which manages the material internal micro structure parameter, ve-locity, and pressure elds simultaneously. The nonlinearity of the corresponding problem, related to the dependency of the diusive stress on the material parameters and the non-linear structure parameter models on the other hand, is treated with generalized Newtons method w.r.t. the Jacobians singularities having a global convergence property.