  We study the problem of static, spherically symmetric, self-gravitating
elastic matter distributions in Newtonian gravity. To this purpose we first
introduce a new definition of homogeneous, spherically symmetric (hyper)elastic
body in Euler coordinates, i.e., in terms of matter fields defined on the
current physical state of the body. We show that our definition is equivalent
to the classical one existing in the literature and which is given in
Lagrangian coordinates, i.e., in terms of the deformation of the body from a
given reference state. After a number of well-known examples of constitutive
functions of elastic bodies are re-defined in our new formulation, a detailed
study of the Seth model is presented. For this type of material the existence
of single and multi-body solutions is established.
