Wire and arc additive manufacturing (WAAM) is a promising alternative to traditional subtractive manufacturing for fabricating large aerospace components that feature high buy-to-fly ratio. Since the WAAM process builds up a part with complex geometry through the deposition of weld beads on a layer-by-layer basis, it is important to model the geometry of a single weld bead as well as the multi-bead overlapping process in order to achieve high surface quality and dimensional accuracy of the fabricated parts. This study firstly builds models for a single weld bead through various curve fitting methods. The experimental results show that both parabola and cosine functions accurately represent the bead profile. The overlapping principle is then detailed to model the geometry of multiple beads overlapping together. The tangent overlapping model (TOM) is established and the concept of the critical centre distance for stable multi-bead overlapping processes is presented. The proposed TOM is shown to provide a much better approximation to the experimental measurements when compared with the traditional flat-top overlapping model (FOM). This is critical in process planning to achieve better geometry accuracy and material efficiency in additive manufacturing.