  In this work wormholes in viable $f(R)$ gravity models are analysed. We are
interested in exact solutions for stress-energy tensor components depending on
different shape and redshift functions. Several solutions of gravitational
equations for different $f(R)$ models are examined. Found solutions imply no
need for exotic material, while this need is implied in the standard general
theory of relativity. Simple expression for WEC violation near the throat is
derived and analysed. High curvature regime is also discussed, as well as the
question of the highest possible values of Ricci scalar for which WEC is not
violated near the throat, and corresponding functions are calculated for the
several models. The approach here differs from the one that has been common
since no additional assumptions to simplify the equations are made, and
functions in $f(R)$ models are not taken to be arbitrary functions, but rather
a feature of the theory that has to be evaluated on the basis of consistency
with observations for the Solar System and cosmological evolution.
