Composites have proven their great potential for many aerospace applications, where high performance justifies high cost. One of the potential applications of composites is helicopter landing gears. Helicopter landing gears consist of straight and curved tubes. A new analysis and design tool is required to consider the manufacturing technology. In this study, high-order analytical methods are proposed to analyze and design thick laminated orthotropic straight and curved tubes subjected to different boundary and loading conditions. In the first part of this thesis, the elasticity displacement field of thick laminated composite straight tubes is developed. In this investigation, thick composite cantilever tubes under transverse loading are studied using the newly displacement-based method. This method provides a quick, convenient and accurate procedure for the determination of 3D stresses in thick composite straight tubes subjected to both bending and shear loadings. In addition, this method is used to study stress and strain distributions in thick composite straight tubes with different simple and complex lay-up sequences. Note that thick laminated composite straight tubes subjected to cantilever loading conditions are investigated for the first time. Moreover, the developed method is used to analyze thick laminated composite straight tubes subjected to different mechanical loadings such as axial force, torque and bending moment. In the second part of this thesis, the general displacement field of thick laminated composite curved tubes is developed. By proposing a new high-order displacement-based method, single-layer composite curved tubes are examined. First, a displacement approach of Toroidal Elasticity is chosen to obtain the displacement field of single-layer composite curved tubes. Then, a layer-wise method is employed to develop the most general displacement field of elasticity for thick arbitrary laminated composite curved tubes. The developed method is used to analyze single-layer and laminated composite curved tubes subjected to pure bending moment. Note that displacement-based Toroidal Elasticity is applied to study thick laminated composite curved tubes for the first time. In addition, the failure analysis on thick composite curved tubes subjected to pure bending moment is conducted. Effects of lay-up sequences of composite curved tubes on stress distributions and failure sequences are investigated, as well. The accuracy of the proposed methods is verified by comparing the numerical results obtained using the proposed methods against finite element method, experimental data and solutions available in the literature. The methods that proposed in this thesis do not require meshing. They simplify greatly inputs that the user has to do, once the program for solution is available. This presents a clear advantage over FEM. Therefore, the most important advantage of the proposed methods is that inputs for modeling and analyzing of composite straight and curved tubes with complex lay-up sequences are simple, easy to use and fast to run. In addition, using FEM for the parametric study is cumbersome. By applying the proposed methods, the parametric study for thick laminated composite straight and curved tubes is simple with low computational cost.