  The paper is concerned with the Einstein equations for a spherically
symmetric static distribution of anisotropic matter. The equations are cast
into a system of Fuchsian type ODE for certain scalar invariants of the strain.
And then the existence and regularity of this ODE is studied under general
constitutive relation. In the case the constitutive relation is given by a
quadratic form of strain, it is also shown that the solutions stay regular up
to the boundary of the material ball.
