Although, undoubtedly, numerical computations are the computations of primary importance in computational mechanics, nevertheless, symbolic computations also constitute a significant related tool. Here at first an extensive review of the major computer algebra systems is made, i.e. (in alphabetical order) of Derive, Macsyma, Maple, Mathematica and Reduce. Next, several applications of symbolic computations to computational mechanics are mentioned in brief (including the computer algebra system used in each of them) as well as the related very recent research results by the author. Extensive conclusions with respect to the usefulness of computer algebra systems in computational mechanics are also mentioned and several comments concerning the trends and the possibilities in this very interesting application of computer algebra systems are made.