We define a topological number and clarify its role played in two-dimensional anisotropic σ models. Non-dissipative metastable states are obtained as counter-examples to which Derrick's theorem cannot be applied. Each metastable state classified by the topological number q turns out to carry |q| vortices and |q| stagnation points for the cases of XY-like anisotropy and to involve |q| antiparallel core spins for those of Ising-like one. The range and strength of vortices are studied in detail for the XY-model obtained from present systems.