This paper is concerned with the static and dynamic bifurcation phenomena exhibited by an elastic panel subjected to an axial load and a fluid flow along its surface (follower force). It is assumed that the system involves two independent parameters, and attention is focused on a special parameter combination, leading to a critical point characterized by a two-Fold zero eigenvalue (of index one), at which both static and dynamic bifurcation may take place in the neighborhood of such a singularity. Divergence boundary, dynamic bifurcation boundary are determined in explicit terms by applying the formula type results of the intrinsic harmonic balancing method. Finally numerical simulation is also applied to verify the analytical results obtained.