Flows with stagnation points, very challenging in analysis, are interesting and important phenomenon in fluids. We first prove a Liouville type theorem for Poiseuille flows for steady Euler system in an infinitely long strip. Because of stagnation points, the nonlinearity of the semilinear equation corresponding to the steam function is not Lipschitz continuous which makes it hard to apply classical analysis methods. In addition, a class of steady incompressible Euler flows, tending to Poiseuille flows in the upstream, are proved to be unique and exist in an infinitely long nozzle via variational approach. This is a joint work with Professor Congming Li and Professor Chunjing Xie.