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Linear viscoelasticity theory is used to analyze the dynamic stability of composite, viscoelastic flat plates subjected to in-plane, biaxial edge loads. In deriving the associated governing equations, a hereditary constitutive law is assumed. In addition, having in view that composite-type structures exhibit weak rigidity in transverse shear, the associated governing equations account for the transverse shear deformations, as well as the transverse normal stress effect. The integro-differential equations governing the stability are solved for simply-supported boundary conditions by using the Laplace transform technique, thus yielding the characteristic equation of the system. In order to predict the effective time-dependent properties of the orthotropic plate, an elastic behavior is assumed for tile fiber, whereas the matrix is considered as linearly viscoelastic. In order to evaluate the nine independent properties of the orthotropic viscoelastic material in terms of its isotropic constituents, the micromechanical relations developed by Aboudi [24] are considered in conjunction with the correspondence principle for linear viscoelasticity. The stability behavior analyzed here concerns the determination of the critical in-plane normal edge loads yielding asymptotic stability of the plate. The problem is studied as an eigenvalue problem. The general dynamic stability solutions are compared with their quasi-static counterparts. Comparisons of the various solutions obtained in the framework of the Third Order Transverse Shear Deformation Theory (TTSD) are made with its first order counterpart. Several special cases are considered and pertinent numerical results are compared with the very few ones available in the field literature. / Master of Science