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; however, such behavior does not match observations from physical soil tests. It leads to poor estimates of walking rate per cycle and over design. In this paper, the impact of a tri-linear (3L) soil idealization accounting for a peak break-out behavior on pipeline walking is investigated. Different shapes and properties of tri-linearity (within the peaky soil range) have been considered leading to an innovative analytical solution. The new solution improves understanding of the main properties involved in the peaky tri-linear soil behavior by providing a set of analytical expressions for pipe walking, which were bench-marked and validated against a set of finite element analyses.