Reduced order models are developed for fully coupled structural-acoustic unsymmetric matrix models, resulting from Cragg's displacement/pressure formulation, using Krylov subspace techniques. The reduced order model is obtained by applying a Galerkin and Petrov-Galerkin projection of the coupled system matrices, from a higher dimensional subspace to a lower dimensional subspace, while matching the moments of the coupled higher dimensional system. Two such techniques, based on the Arnoldi algorithm, focusing on one-sided and two-sided moment matching, are presented. To validate the numerical techniques, an ABAQUS coupled structural-acoustic Benchmark problem is chosen and solved using the direct approach. First, the physical problem is modeled using ANSYS FE package and compared with closed form solutions. Next, ANSYS results are compared with nodal velocities obtained by generating reduced order models via moment matching. The results show that the reduced order models give a very significant reduction in computational time, while preserving the desired accuracy of the solution. It is also shown that the accuracy of the one-sided method could be further improved by using two-sided methods, where the Arnoldi vectors are optimized for chosen outputs. The accuracy of the approaches, convergence models, and computational times are compared.