Offshore pipelines used for transporting hydrocarbons are cyclically loaded by great variations of pressure and temperature. These variations can induce axial instability in such pipelines. This instability may cause the pipelines to migrate globally along their length; an effect known as pipeline walking. Traditional models of pipeline walking have considered the axial soil response as rigid-plastic (RP); however, such behavior does not match observations from physical soil tests. It leads to inaccurate estimates of walking rate (WR) per cycle and over design. In this paper, a trilinear (3L) soil resistance model is used to represent seabed resistance to investigate the behavior of pipeline walking. Different parameters, i.e., shapes and properties of trilinearity (within the peaky soil model type), have been considered leading to a closed-form solution. This solution improves the understanding of the main properties involved in the peaky trilinear soil behavior by providing a set of analytical expressions for pipe walking, which were benchmarked and validated against a set of finite element analyses.