Currently, numerically simulated synthetic seismograms are widely used by seismologists for seismological inferences. The generation of these synthetic seismograms requires large amount of computing resources, and the maintenance of these observed seismograms requires massive storage. Traditional high-performance computing platforms is inefficient to handle these applications because rapid computations are needed and large-scale datasets should be maintained. The emerging cloud computing platform provides an efficient substitute. In this paper, we introduce our experience on implementing a computational platform for rapidly computing and delivering synthetic seismograms on Windows Azure. Our experiment shows that cloud computing is an ideal platform for such kind of applications.