Consideration is given to the mutual effect of pipeline bending, internal and external pressures, compression force effect, fluid flow along the pipeline with pre-assigned density, axisymmetric expansion of the pipe and its longitudinal contraction, change in the pipe wall temperature, and formation of arched ejections. An elastic pipeline is fixed on clamped sliding supports which do not hinder the fluid flow inside the pipeline along its axis. On the supports, both the deflection and the rotation angle are equal to zero. The pipeline is subjected to longitudinal compression. Compression force, pressures inside and outside the pipeline and velocity of fluid flow along the pipeline change independently of each other. This research treats the static interaction of instabilities depending on compression force, internal and external pressures, velocity of fluid flow, axisymmetric expansion of the pipe, and change in the pipe wall temperature. Flexural stiffness, tensile forces and external hydrostatic pressure stabilize the pipeline, while compression forces, internal hydrostatic pressure, fluid motion at any velocity inside the pipeline and an increase in the pipe wall temperature destabilize it. With an increase in the yield point of the pipeline material and the distance between the supports, the acceptable amplitude of arched ejection increases as well. With an increase in the internal pressure of the pipeline, the acceptable amplitude of arched ejection tends to be reduced. The obtained results enable analyzing the stability of pipeline systems. These results can be applied to analyzing static stability of pipelines at the stage of design, performance and elimination of arched ejections.