The underwater suspended pipeline was investigated for the dynamic instability which is applied at the problem for the oscillation of the pipe-line part by inverted pendulum. The connection point of pendulum was received as vertical moving point by harmonic law. For definition of the dynamical equation it is used the analogy of the Mathieu equation. For solution it is used Ince-Strut diagram. As numerical example it was used the pipeline behavior at the project between Turkey and North Cyprus at the East Mediterranean Sea.