The use of parallel computers makes simulation of elastic waves feasible throughout large structures by means of recent advances in domain decomposition methods. We introduce a competitive parallel algorithm for the propagation of elastic waves in complex heterogeneous media using finite-element discretization. This parallel method, called the multiblock method, performs more efficiently than classical domain decomposition techniques based on substructuration, such as the Schur complement technique. It reduces considerably the amount of communication amongst processors because the interface problem between subdomains is solved by taking advantage of Huygens' principle for wave propagation. We provide some numerical examples and detailed studies on the efficiency and performance of the algorithm, proving that it is competitive and less costly, from the computational viewpoint, than algorithms based on the Schur technique.