The paper is an analytical review concerned with a spherically symmetric static problem of General Relativity (GR) in application to continuum. This problem is of special interest for the theory, because it can be reduced to ordinary differential equations whose solutions are applied to describe cosmological models. The formulation of the problem is analyzed with respect to completeness and solvability of GR equations. Spherically symmetric static problems are considered for vacuum, perfect incompressible or compressible fluids and elastic solids within the framework of classical mechanics, linearized GR equations, traditional Schwarzchild space geometry and the special Riemannian space which is Euclidean with respect to the space coordinates and Riemannian with respect to the time coordinate only.