Failure stresses due to centrifugal forces in circular plates of general polar anisotropy are determined. The plate was assumed to be symmetrically laminated, each lamina being oriented at an arbitrary angle with respect to the radial coordinate. Since the plate considered had unconstrained and stress-free outer boundary, it was possible to obtain closed-form solutions for radial and circumferential displacements. The intralaminar failure stresses are then calculated and, using the Tsai-Wu tensorial failure theory, the safety factors for each lamina interface has been determined. The material used for numerical results was chosen arbitrarily for purely illustrating purposes. The results have shown that it was preferable, solely for the increased strength purposes, to have fibers placed in radial direction for the particular material and the lay-up chosen.