Reducing production scrap is vital for decarbonizing the aluminum industry. In extrusion, the greatest source of scrap stems from removing profile sections containing transverse (charge) welds that are deemed too weak for their intended purpose. However, until now, there has been no predictive transverse weld strength model. This article establishes a transverse weld strength model as a function of billet properties and extrusion parameters. It extends the film theory of solid-state welding by enhancing Cooper and Allwood's plane strain model to consider non-plane strain deformations at the billet-billet interface. These enhancements are informed by analyzing oxide fragmentation patterns through shear lag modeling and microscopy of profiles extruded from anodized billets. Model predictions are assessed through shear tests on welds from single and two-piece billets, extruded into rod, bar, and multi-hollow profiles. The experiments reveal that negative surface expansions at the weld nose cause interface buckling and weaker welds, but both surface expansions and weld strengths increase with distance from the nose. In non-axisymmetric profiles, deformation conditions and strengths vary across, as well as along, the weld. Two-piece billet welds are longer but reach bulk strength long before weld termination. The model predicts these trends and shows that die pressures are sufficient for micro-extrusion of any exposed substrate through interface oxide cracks. This underscores the significance of interface strains in exposing substrate and determining the weld strength. The model can help increase process yields by determining minimum lengths of weak profile to scrap and aiding process optimization for increased weld strength.