Equilibrium equations on Zero Extension Lines (ZEL, lines with zero linear strain) are important ii soil engineering because a suitable displacement field (network of ZEL) is often more: practical for geomechanics problems. The stress characteristic equilibrium equations for soil, having an angle of friction phi and cohesion c are available on the stress characteristics field. However, because the ZEL field is distinct, the stress characteristic equations do not apply on ZEL. In this paper, equations of equilibrium are derived on zero extension lines. In addition, the application of equilibrium equations on ZEL to the static bearing capacity of clay, seismic bearing capacity of clay soils and dynamic lateral pressure on retaining walls is presented.