Modeling, numerical analysis, and optimization of ceramic paste extrusion for extrusion-based additive manufacturing of the high-value products will be carried out in the present project. The modified Navier-Stokes equations for non-Newtonian fluid flow with temperature dependent stress tensor on time-dependent domains will be used to model extrusion in a ram extruder. The model equations will be solved using a finite element method with equal order interpolation and local projection stabilization and a priory finite element error estimates will be derived. The arbitrary Lagrangian-Eulerian methods will be used to discretize problems on time-dependent domain. The rheological properties of ceramic pastes made from local materials will be measured. The developed finite element solvers will be validated against experimental data collected in a custom-build extruder. The constructed finite element solvers will be used to find the optimal extrusion process parameters and extruder geometries.