Abstract: Based on geometrical non-linearity, considering the influence of equivalent axial force (S₀ ) on the deflection of pipeline,the paper presented the equations with or without anchor blocks at both ends for calculating static and dynamic strengths of aerial crossing pipelines. The equations for the pipelines with anchor blocks are explicit. As for the pipelines without fixed anchors at both ends, it is regarded that the lateral and longitudinal resistance of soil to buried pipelines is proportional to the lateral and longitudinal displacements of pipelines, respectively.Calculations of internal forces and deformations are reduced to the solution of two nonlinear equations, and natural frequencies
of pipelines are determined from the characteristic equations.The explicit criterion S₀ either compressive or tensional was presented. The paper described the verified examples of the static and dynamic strengths.

Key words: oil and gas gathering, pipeline aerial crossing, buried pipeline, strength, natural frequency, calculation, equation