The method of searching the embeddings of Riemannian spaces with a high enough symmetry in a flat ambient space is suggested. It is based on a procedure of construction of surfaces with a given symmetry. The method is used for the construction of the embeddings for the Schwarzschild solution in a six-dimensional ambient space and Friedmann-Robertson-Walker solutions in five-dimensional ambient space. All known variants of embeddings for these spaces are constructed using this method. Two new embeddings for Schwarzschild solution are constructed also. One of these new embeddings is asymptotically flat, while the other embeddings in a six-dimensional ambient space do not have this property. The asymptotically flat embedding can be used in the analysis of the many-body problem, as well as for the development of gravity description as a theory of a surface in a flat ambient space.