New materials such as biopolymers derived from vegetables are increasingly attractive for various applications, particularly in the biomedical, pharmaceutical, and food sectors. New methods for producing parts from these materials are required, and additive manufacturing is among the most common due to its simplicity, speed, and ability to produce complex shapes. To understand the behavior of a zein-based biopolymer—zein being a protein derived from maize—during an additive manufacturing process using fused filament fabrication, it was necessary to model the coalescence process between layers. A 3D model based on the Finite Element Method (FEM) and the Level Set method was developed to study the sintering process between four filaments of zein plasticized with 20 wt% glycerol.