Pipelines can be subjected to bending loads due to a variety of factors such as seismic activity, slope instability, or discontinuous permafrost. Experimental studies of Sen et al. [1–3] showed that pipelines can fail under bending loads due to pipe body tension side fracture which is a mostly overlooked failure mode in pipelines. Recent numerical studies on the structural behavior of cold bent pipes [4–6] also confirmed the likelihood of the pipe body tension side fracture. Furthermore, it was shown that both the material properties and the level of internal pressure can have a considerable effect on the failure mode of the pipe. In this current work, the parametric studies of internal pressure and material properties are extended to straight pipes using finite-element analysis. The differences in the structural behavior due to using stress–strain curves from test specimens in longitudinal and circumferential direction of the pipe are demonstrated. Using failure criteria based on the equivalent plastic strain, different failure modes corresponding to different levels of internal pressure and yield strength are shown on straight pipes.