  In this paper, exact wormhole solutions in the context of $f(R)$ theory of
gravity are investigated. Since the Einstein field equations are modified in
3+1 dimensions in the $f(R)$ theory of gravity, we have studied some possible
solutions with different forms of shape function and $f(R)$ function. We show
that choosing $f(R)$ or metric functions arbitrarily may lead to a conflict for
wormhole solutions. Some previous solutions are discussed which verify the
contradiction throughout the equations. We conclude that wormhole solutions in
the context of $f(R)$ gravity should be revisited.
