Materials that display both fluid and solid-like behavior can be seen in a variety of applications ranging from food processing to oil extraction. In this work, we present three-dimensional simulations of elastoviscoplastic fluids, Carbopol at several concentrations, filling the space enclosed by two parallel vertical plates and a horizontal boundary. To describe the rheology of the fluid, we use the Herschel-Bulkley Saramito (HBS) constitutive model [1]. This model describes the fluid as a shear-thinning viscoelastic fluid above yield and an elastic solid below yield, where the yield criterion is based on the von Mises stress. Equations for momentum, mass, and stress are solved using the finite element method coupled to an arbitrary Lagrangian-Eulerian mesh movement algorithm. We compare three-dimensional mold filling simulations to flow visualization experiments of the flow scenarios considered and extend our previously published work [2]. The experimental data is shown to be self-similar - maintaining a hemispherical shape over time, with data collapsing to a single curve given the correct scaling. For three-dimensional computations, the HBS model is generally predictive of the shape of the growing fluid droplet compared to the experimental droplet shapes and predicts this self-similarity. However, for higher flow rates, slip at the contact line, necessary for mesh stability, lead to over prediction of the width. We will also discuss some recent work coupling the HBS model to a level set method.