Doctor of Philosophy / Department of Civil Engineering / Hayder A. Rasheed / The use of laminated composites in aerospace, automotive, and civil engineering applications is ever growing due to their distinguished properties (High stiffness-to-weight ratio, high strength-to-weight ratio, fatigue and corrosion resistance). This growth has resulted in increasing the demand for better understanding the mechanics of laminated composites. Composite columns and wide plates, like any traditional members subjected to axial compression, undergo stability issues prior to failure. Limited amount of research studies has focused on the buckling of laminated anisotropic composite members. Analytical formula for the buckling load of generally anisotropic laminated composite simply supported thin columns and wide plates is derived using the Rayleigh Ritz approximation and bifurcation approach. The effective axial, coupling and flexural stiffness coefficients of the anisotropic layup is determined from the generalized constitutive relationship using dimensional reduction by static condensation of the 6x6 composite stiffness matrix. The resulting explicit formula is expressed in terms of the generally anisotropic material properties as well as the member geometry. The developed formula may be considered an extension to Euler buckling formula using Rayleigh-Ritz approximation and the first of its kind since Euler. This formula reduces down to Euler buckling formula once the effective coupling stiffness term vanishes for isotropic and certain classes of laminated composites. The analytical results are verified against finite element Eigen value solutions for a wide range of anisotropic laminated layups yielding high accuracy. Comparisons with experiments; conducted at Kansas State University for the simply supported case, are also performed showing good correspondence. A brief parametric study is then conducted to examine the effect of ply orientations and material properties including hybrid carbon/glass fiber composites, element thickness, and element type in FE analysis. Relevance of the numerical and analytical results is discussed for all these cases.