  This paper is devoted to a fundamental system of equations in Linear
Elasticity Theory: the famous Lam\'e-Navier system. The Clifford algebra
language allows us to rewrite this system in terms of the euclidean Dirac
operator, which at the same time suggests a very natural generalization
involving the so-called structural sets. We are interested in finding some
structures in the solutions of these generalized Lam\'e-Navier systems. Using
MATLAB we also implement algorithms to compute with such partial differential
operators as well as to verify some theoretical results obtained in the paper.
