A Grid-enabled asynchronous metamodel-assisted evolutionary algorithm is presented and assessed on a number of aerodynamic shape optimization problems. An efficient way of implementing surrogate evaluation models or metamodels (artificial neural networks) in the context of an asynchronous evolutionary algorithm is proposed. The use of metamodels relies on the inexact pre-evaluation technique already successfully applied to synchronous (i.e. generation-based) evolutionary algorithms, which needs to be revisited so as to efficiently cooperate with the asynchronous search method. The so-created asynchronous metamodel-assisted evolutionary algorithm is further enabled for Grid Computing. The Grid deployment of the algorithm relies on three middleware layers: GridWay, Globus Toolkit and Condor. Single- and multi-objective CFD-based designs of isolated airfoils and compressor cascades are handled using the proposed algorithm and the gain in CPU cost is demonstrated.