The United States Air Force is interested in the development of hypersonic and reusable space vehicles. A significant factor in the pursuit of that goal is to develop the critical materials and structures necessary to withstand the expected aerodynamic heating, as well as the aeroacoustic and engine induced acoustic loading. This study focused on the geometric nonlinear response of these fully clamped, tapered CMC panels to stationary Gaussian random base excitation. The taper of the selected CMC panel was asymmetric resulting in an expected coupling of the axial and bending response. The power spectral densities (PSDs), amplitude, peak and rainflow probability density functions (PDFs), time-history response, and axial, bending and total strain contributions to narrowband random vibration testing were investigated, noting the effects of the geometric nonlinearities. Several interesting phenomenon resulted from the study. First, the effects of the coupling between the axial and bending strain on the response PSDs were highlighted. Next, the study indicated a distinct asymmetry in the narrow-band response PDFs due to the increasing significance the axial strain played in the total response. Finally, the mean total, bending and axial strain response were noted to exhibit a quadratic relationship with respect to the excitation level.