As part of a research work on the fatigue of free spanning subsea pipelines, the maximum longitudinal stress at or near mid-span and that at support are solved with finite element method for a 10" flow line and a 20" export line under different span length and support conditions. The maximum longitudinal stresses are also calculated for some cases of a two-span flow line. These stresses serve as intermediate results to be used in combination with other data such as pipeline frequency, wave and current velocity for the fatigue evaluation of subsea pipelines. Stress results of single span pipelines show that the maximum longitudinal stress decreases as the span length increases. The maximum stress at the fixed end in the fixed/fixed boundary case is the largest while the maximum at mid-span of pinned/pinned case the smallest among the obtained maximum stresses. The two-span flow line results show that the support length does not have significant effect on the maximum stress.