  Conformally flat spacetimes with an elastic stress energy tensor given by a
diagonal trace-free anisotropic pressure tensor are investigated using 1+3
formalism. We show how the null tetrad Ricci components are related to the
pressure components and energy density. The 1+3 Bianchi and Jacobi identities
and Einstein field equations are written for this particular case. In general
the commutators must be considered since they supply potentially new
information on higher order derivatives of the 1+3 quantities. We solve the
system for the non rotating case which consist of ODEs of a spatial coordinate.
