Corrosion or manufacture defects can cause internal cracks in steel pipes. For ductile materials, the crack front can yield before the stress intensity reaches its fracture toughness. The yielding of the crack front could ease the stress concentration at the crack front. Therefore, to predict the failure of cracked steel pipes using linear elastic fracture mechanics it is necessary to quantify the part of fracture toughness that withstands the elastic stress field, namely, elastic fracture toughness. This paper intends to propose an analytical model of the elastic fracture toughness for steel pipes with internal surface cracks.