  The solutions for the field equations of $f(R)$ gravity are investigated in
static cylindrically symmetric space-time. Conserved quantities of the system,
as well as unknown functions, can be determined with the help of the Noether
symmetry method. In this article, some unknown values of the equations of state
parameter (EoS) have emerged as a result of the constraints obtained by
analyzing the Noether symmetry equations for the $f(R)=f_0 R$ case.
Consequently, several new exact solutions have been found for cases of General
Relativity in static cylindrically symmetrical space-time for the non-dust
matter.
