  This work is devoted to the study of analytic wormhole solutions within the
framework of $f(R)$ gravity theory. To check the possibility of having wormhole
structures satisfying energy conditions, by means of the class I approach the
pair $\{\Phi(r), b(r)\}$ describing the wormhole geometry has been obtained.
Then, in conjunction with a remarkably $f(R)$ gravity model, the satisfaction
of the null and weak energy conditions at the wormhole throat and its
neighborhood is investigated. To do so, some constant parameters have been
bounded restricting the space parameter. In this concern, the $f(R)$ gravity
model and its derivatives are playing a major role, specially in considering
the violation of the non--existence theorem. Furthermore, the shape function
should be bounded from above by the Gronwall--Bellman shape function, where the
red--shift function plays a relevant role. By analyzing the main properties at
the spatial stations and tidal accelerations at the wormhole throat,
possibilities and conditions for human travel are explored.
