Three problems of stability loss are investigated and corresponded buckling modes are discussed. The first one is the stability loss of a compressed transversely isotropic linearly elastic medium. The standard analysis based on the Hadamard condition is conducted to solve this problem. The critical compression could be uniquely defined from the bifurcation equations but not a wave length. So, the buckling mode remains generally indefinite. The second considered problem is the stability loss of a compressed half-space with a free surface. It could be shown that the waviness is localized near the free plane surface but as for an entire space the wave length and the buckling mode are indefinite. These problems are treated in linear and nonlinear statement. In linear approach the pre-buckling deformations are ignored. It is shown that for some values of parameters the linear approach leads not only to the numerical error but also to qualitatively incorrect results. The thisrd problem under investifation is the stability loss of an uniformly compressed plate lying on a soft elastic half-space. In this problem the wave length is uniquely defined. Using the nonlinear post-critical analysis it is shown that the buckling mode could be fully defined and is has a chessboard-like character.