All the possible equivalent barotropic (EB) laminar solutions are firstly explored,and all the possible non-EB elliptic circulations and hyperbolic laminar modes of rotating stratified fluids are discovered in this paper.The EB circulations (including the vortex streets and hurricane like vortices) possess rich structures,because either the arbitrary solutions of arbitrary nonlinear Poisson equations can be used or an arbitrary two-dimensional stream function is revealed which may be broadly applied in atmospheric and oceanic dynamics,plasma physics,astrophysics and so on.The discovery of the nonEB modes disproves a known conjecture.