When one deals with infinite homogeneous media, one can use spatial Fourier transforms for physical quantities, and as a consequence one obtains a ground state which is periodic such as a ferromagnetic one, an antiferromagnetic one or a helical one. Now, when considering finite samples which may also have some internal detects, physical quantities are no longer periodic ones and the ground state differs from that of the infinite material by what we call a “rearrangement”. We have already studied such magnetic rearrangements for simple geometries: thin films with a magnetic easy axis normal to the surface, simple cubic samples, {001} surface and only nearest neighbor exchange and anisotropy coupling [1]. The result of this microscopic study is that magnetic rearrangements near the surface are quite general. As a matter of fact it confirms a lot of experimental evidence: on the one hand the first measurements of magnetization in thin films [2], with what may be considered now as a poor vacuum, showed a large spread in the results, on the other hand, recent measurements [3,4] of samples in high vacuum, or with coating molecules in a given quantity have shown that the influence of the surface structure upon the magnetization deepens inside the sample. Our purpose here is to determine the magnetic ground state for arbitrary samples. Of course such a general determination cannot be achieved at a very microscopic level, so we use here a continuum model, which may be completed by solutions of continuity in order to take into account solutions which give rise to ferrimagnetism for instance, for infinite samples. That defines the three parts of this paper. First we derive the general determination of the ground state in a continuum model by means of a variational method. Secondly, we show that in a lot of usual cases, the ground state takes the form of a frozen wave. A last part is devoted to the applications to different kinds of coupling and to various defects.