In this dissertation, a theoretical/numerical methodology is presented for coarse and fast predictions of cabinet vibrations. The study is focused on vibrations of rib-stiffened panels by improving a smearing technique and employing it into finite element modeling. The computationally efficient smearing technique for a cross-stiffened flat thin rectangular plate has been known for many years, but so far the accuracy of predicted natural frequencies has been inadequate. To improve predictions, all stiffeners including the ones neglected in the ordinary smearing technique are taken into account in the calculation of bending stiffness in this dissertation. The improved smearing technique results in good accuracy for predicted natural frequencies and forced vibrations of flat stiffened plates. Another improvement concerns the orientation of the stiffeners. The original smearing technique presupposes that the stiffeners are parallel to the edges of the plate, but simple considerations make it possible to relax this requirement. Whereas the improved smearing technique is well established for stiffened flat panels, there is no similar established technique for doubly curved stiffened shells. In an additional study, the improved smearing technique is combined with the equation of motion for a doubly curved thin rectangular shell, and a solution is offered for using the smearing technique for stiffened shell structures. Finally, the developed smearing technique is employed in a finite element modeling for estimating the vibrational properties and associated sound radiation of models including stiffened panels. Overall, the developed technique is found to be a good method for fast estimations of cabinet vibrations.