Abstract: On condition that: (1)the "elastic flexual hinge" model is used, with soil reaction to elbow neglected and internal pressure subjected to the elbow concerned; (2)the longitudinal soil force vs pipeline displacement is bilinear, that is, elastic section and limit equilibrium section(plastic)are discriminated; (3)the lateral soil force is proportional to the lateral displacement of pipeline; (4)the straight pipes connected tangen-tially with elbows are simplified as semi-infinite beams and/or rods; (5)temperature differences along with pressure are taken into account. New formulae for calculating bending moment of buried elbows are derived. The new calculation results are compared with those based on the recommended formulae in the oil-and-gas pipeline design specifications. The checking methods for the strength of buried elbows and determination methods of soil-pipe interaction parameters are disscussed. Practical strength design formulae for pipelines with elbows are recommended.