This paper investigates the stability of deformable layers produced by material extrusion additive manufacturing. A Computational Fluid Dynamics (CFD) model is developed to predict the deposition flow of viscoplastic ma­ terials such as ceramic pastes, thermosets, and concrete. The viscoplastic materials are modelled with the Bingham rheological equations and implemented with a generalized Newtonian fluid model. The developed CFD model applies a scalar approach to differentiate the rheology of two layers in order to capture the deposition of a wet layer onto a semi solidified printed layer (i.e., wet-on-semisolid printing). The semi solidification is modelled by a yield stress buildup. The cross-sectional shapes of the deposited layers are predicted, and the relative deformation of the first layer is studied for different yield stress buildups and processing conditions such as printing- and extrusion-speed, layer height, and nozzle diameter. The results of the CFD model illustrate that the relative deformation of the first layer decreases non-linearly with an increase in yield stress, and that stable prints can be obtained when taking into account the semi solidification. Furthermore, it is found that the deformation is dependent on a non-trivial interplay between the extrusion pressure, the shape of the cross-section, and the contact area between the layers. Finally, the results highlight which process conditions can be changed with benefit in order to limit the requirement on the yield stress buildup and still provide stable prints.