In this paper, a new asynchronous iterative sub-structuring method is presented. This method is based on a classical sub-structuring approach, but during the iterations of the algorithm, at the end of each iteration the synchronisation between the processors is here removed leading to totally asynchronous iterations. The mathematical proof of the convergence of this new asynchronous iterative sub-structuring method is first introduced, followed by an example of the parallel implementation. Numerical results performed on a three dimensional test case illustrate the robustness, performance and efficiency of the asynchronous version over its synchronous counterpart.