Abstract: The maximum axial force on long distance buried pipeline heating transportaion takes place in anchor section. The strength destruction phenomina wasn't apparently found in practice as the equivalent stress frequently exceeds the yield strength in an anchor section, which indicated that the design strength is of potential. The new concept of "constrain degree" presented in reference 〔1〕 is significant.The primary theory in the paper through quantitative analysis of elastic deformation, from the other point, probes into the stess potential in anchor section, provides together reference to the economic benefic on pipeline design.