Vibroacoustic characteristics of multidirectional stiffened laminated plates with or without compliant layers are explored in the wavenumber and spatial domains with the help of the two-dimensional continuous Fourier transform and discrete inverse fast Fourier transform. Implicit equations of motion for the arbitrary angle ply laminated plates are derived from the three-dimensional higher order and Reddy third order shear deformation plate theories. The expressions of acoustic power of the stiffened laminated plates with or without complaint layers are formulated in the wavenumber domain, which is a significant method to calculate acoustic power of the stiffened plates with multiple sets of cross stiffeners. Vibroacoustic comparisons of the stiffened laminated plates are made in terms of the transverse displacement spectra, forced responses, acoustic power, and input power according to the first order, Reddy third order, and three-dimensional higher order plate theories. Sound reduction profiles of compliant layers are further examined by the theoretical deductions. This study shows the feasibility and high efficiency of the first order and Reddy third order plate theories in the broad frequency range and allows a better understanding the principal mechanisms of acoustic power radiated from multidirectional stiffened laminated composite plates with compliant layers, which has not been adequately addressed in its companion paper. (Cao and Hua, 2012, “Sound Radiation From Shear Deformable Stiffened Laminated Plates With Multiple Compliant Layers,” ASME J. Vib. Acoust., **134**(5), p. 051001.)