Summary: The idea of this article is to examine the effects on dynamics of dissipative gravitational collapse in nonstatic cylindrical symmetric geometry by using Misner-Sharp concept in framework of metric \(f(R)\) gravity theory. In this interest, we extended our study to the dissipative dark source case in both forms of heat flow and the free radiation streaming. Moreover, the role of different quantities such as heat flux, bulk, and shear viscosity in the dynamical equation is evaluated in thorough version. The dynamical equation is then coupled with full causal transportation equations in the context of Israel-Stewart formalism. The present scheme explains the physical consequences of the gravitational collapse and that is given in the decreasing form of inertial mass density which depends on thermodynamics viscous/heat coupling factors in background of \(f(R)\) theory of gravity. It is very interesting to tell us that the motives of this theory are reproduced for \(f(R) = R\) into general theory of relativity that has been done earlier.