We consider the framework of regular word/tree model checking
where sets of configurations of a system 
are represented by regular word/tree languages and its dynamics is modeled 
by a term rewriting system (or a  regular word/tree transducer). 
We focus on the computation of the reachability set R*(L)
where R is a regular relation  and L is a regular  language.
The construction of this set is not possible in general.
Therefore, we present a general acceleration technique,
called  regular  widening which
allows, in many cases,  to compute this transitive closure.
This technique can be applied uniformly to different classes of systems. 
Moreover, we show that it  is powerful enough to simulate several existing constructions.