The three-dimensional linearized theory of stability (TDLTS) of deformable solid body mechanics is developed for the investigation of the three-dimensional stability loss problems of elements of constructions fabricated from the time-dependent composite materials. All procedures are made on the plate from the composite material that is modelled as homogeneous anisotropic linear viscoelastic material with normalised mechanical properties. As a stability loss criterion the values of time (critical time) for which the size of the initial imperfection starts to increase and grows indefinitely, is selected. By employing semi-analytical FEM modelling and Laplace transformation the numerical investigations are made. From the analyses of these results it is concluded that they can be significantly different from those obtained in the framework of the third-order refined plate theory. (C) 2001 Elsevier Science Ltd. All rights reserved.