Analyses to estimate the collapse loads indicate that the effect of transverse anisotropy on the collapse loads depends upon the case under consideration. While transverse anisotropy substantially increases the collapse load in the case of solid disks and circular plates under lateral pressure, it has no effect on the collapse load of a circular plate under shear loading. The collapse loads in the case of annular disks and annular plates under lateral pressure may increase or remain constant after an initial increase with respect to transverse anisotropy. This effect depends on the assumed yield criterion. Some similarities in the analysis of the disk and the circular plate are shown.