In this article, a distributed-lumped model is developed for identical pieces of pipes that are welded together, as the main structure of the pipelines. The model can predict the signal amplitude and velocity in high attenuation, where dispersion effects limit the range of the health test. The health test is simulated by sending a torsional-guided wave across the pipe. The wave is attenuated as it passes through the welds, which act as lumped elements, while it becomes significantly dispersed when travelling through the pipe segments, which function as distributed elements. The theoretical shape of the angular displacement and angular velocity signal, in the frequency domain, is calculated and commented upon. The approach herein is the dynamic stiffness matrix method, which is developed for both the velocity and displacement signals. This approach enabled the signal pattern to be found in a 100-m pipe test comprising 8 pipe segments. This range is the current practice in Long Range Ultrasonic Testing (LRUT) of the pipelines. The new approach in this article combines distributed parameters of pipe segments with lumped parameters of welds. Then, it implements the Dynamic Stiffness Matrix Method (DSMM) to pipelines as “Distributed-Lumped” systems. In a numerical example, the results are demonstrated via the frequency response signature of a healthy pipe. This helps the damaged pipe to be designated via comparison with experimental frequency response signatures.