In this paper, three-dimensional finite element (FE) simulations of double SAW and hydrostatic test processes of spirally welded pipes are carried out in two simulation steps using the ANSYS commercial software. In the first step, i.e., welding, a new method, namely, unfurl-mapping (UM) is introduced to overcome the geometrical difficulties of defining the Goldak double ellipsoidal heat source of the welding process. UM virtually opens the pipe into a flat surface, and therefore, the spiral seam is mapped to a straight line. To discretize the pipe, fine brick elements are utilized for meshing the main computational zone. The rest of the model is meshed by coarse shell elements by applying the multi-point constraint technique. This non-uniform mesh structure reduces the computational requirements significantly and provides the ability to simulate the entire pipe. Therefore, in the second step, the hydrostatic test is easily simulated by defining a ramped internal pressure. The method is validated using hole drilling measurements performed before and after hydrostatic test for this research. It is observed that obtained results from the FE simulations are in good agreement with the experimental measurements.