Stiffeners attached to composite panels and shells may significantly increase the overall buckling load of the resultant stiffened structure. Initially, an extensive literature review was conducted over the past ten years of published work wherein research was conducted on grid stiffened composite structures and stiffened panels, due to their applications in weight sensitive structures. Failure modes identified in the literature had been addressed and divided into a few categories including: buckling of the skin between stiffeners, stiffener crippling and overall buckling. Different methods have been used to predict those failures. These different methods can be divided into two main categories, the smeared stiffener method and the discrete stiffener method. Both of these methods were used and compared in this thesis. First, a buckling analysis was conducted for the case of a grid stiffened composite pressure vessel. Second, a buckling analysis was conducted under the compressive load on the composite stiffened panels for the case of one, two and three longitudinal stiffeners and then, using different parameters, stiffened panels under combined compressive and shear load for the case of one longitudinal centric stiffener and one longitudinal eccentric stiffener, two stiffeners and three stiffeners. / Master of Science / Aircraft in flight is subjected to different loads due to maneuvers and gust, external forces cause internal loads, which depends on the location of the panel in the aircraft, those internal loads, may result in the buckling of the panel. There is an imminent need for structural efficiency, strong and lightweight material. Stiffened composite panels is a promising technology capable of addressing those needs. Composite stiffened panels have many advantages including but not limited to, small manufacturing cost, high stability, great energy absorption, superior damage tolerance etc. The main failure modes for stiffened composite panels is buckling. Buckling failure modes could be of a global nature, local skin buckling or stiffener/rib crippling, predicting those failure is of high practical importance and a predominant design criterion. An extensive literature review on buckling of stiffened composite panels was conducted in this thesis. Buckling analysis as well as a parametric study of grid stiffened composite cylindrical shell for a pressure vessel was conducted, an analytical solution was derived and verified using ABAQUS, a Finite Element Software. Buckling analysis as well as a parametric study of stiffened panels with longitudinal stiffeners, under different structural situations, was also conducted and results verified.