The tear test is widely used to measure the fracture toughness of thin rubber sheets and polymer films. More recently, the tear test has been applied to polymer materials produced by melt extrusion additive manufacturing to measure the fracture toughness of a single weld between two printed (extruded) filaments. This paper presents a finite element modeling study of the tearing of a weld between two printed filaments to investigate the mechanics of the tear test and the effects of geometry and material properties on the measured tear energy. The mechanical behavior of the printed filaments was described by a viscoplastic model for glassy polymers and the weld was represented using cohesive surface elements and the Xu–Needleman traction–separation relationship. The geometric model and the material parameters were chosen based on experimental measurements. The tear energy varied with the specimen dimensions, the curvature of the printed filaments, the yield stress relative to the cohesive strength of the weld, and the post-yield stress drop. The effects of the hardening modulus were small. These factors altered the viscoplastic dissipation in the material ahead of the propagating crack tip. The results showed that viscoplastic dissipation could constitute a large fraction of the tear energy and is strongly affected by the specimen dimensions and the geometry and material properties of the printed filament. There was also considerable mode mixty in the tear energy. The findings can be used to design tear tests to measure the intrinsic fracture toughness of the weld.