A first-order shear-deformation plate theory is used to predict the free vibration frequencies and mode shapes in spinning laminated composite plates. The theory accounts for geometric nonlinearity in the form of the von Karman strains and the effects of rotatory inertia. The plate is permitted to have an arbitrary orientation offset from the axis of rotation. A finite element model is developed to obtain numerical solutions to this class of problems. The model is validated by comparing the results for isotropic plates with those available in literature. The natural frequencies and mode shapes of isotropic and laminated composite plates as functions of angular velocity, pitch angle, and sweep angle are presented. Though the expected increase in frequency with angular velocity is observed for most modes, it is seen that there is a decrease in the free vibration frequency with angular velocity for torsional modes of swept and pitched plates. 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.