In the present thesis, the linear and geometrically nonlinear response of plates and shells with general shape under various loadings and boundary conditions () are considered. The governing equilibrium and compatibility equations of the plates and shells are developed using Degenerated Shell method incorporating the nonlinear terms of strain components. The obtained system of nonlinear differential equations is solved by means of finite strip method (FSM). The deformation components and geometry of the shell in the finite strip element are estimated by Lagrangian functions in the transversal directions. In the longitudinal direction of the strip B-spline basis functions are employed which are used in isogeometric analysis (IGA). Therefore, the proposed method in the present thesis is nominated isogeometric B-spline finite strip method (IG-SFSM). Consequently, the proposed method is an upgraded version of FSM in comparison to the other versions, which can model the shells with more complicated geometries, deformation field and BCs. In order to determine the level of credibility of the corresponding formulation developed in the present thesis, several examples incorporating various geometries, BCs, loadings and materials are considered and the corresponding results are compared with the results which are available in the references. The main target of the present study is to extend the last versions of FSMs to carry out various analyses of the shells, eliminate their limitations related to geometry, loading and BCs and reduce the computational efforts. The formulation of the proposed method incorporates isotropic, laminated composite and sandwich functionally graded materials (FGMs). The obtained results are classified in four different groups. In the first step the linear static analysis of the shells incorporating deformation field and stress analysis, is carried out. Then, second-order analysis of the shells (initial buckling) with various geometries and BCs are performed. In the third group of results, free vibration analysis of the shells is considered. Finally, geometrical nonlinear analysis of the shells for various conditions is carried out and the obtained results are compared with the corresponding IGA, EFG and FEM results. The obtained results in the present study showed that by using the proposed method in the problems corresponding to linear static, free vibration, buckling and geometrical nonlinear analyses of the shells, it is possible to reduce the computational costs with acceptable accuracy comparing to the other numerical methods such as mesh-free and finite element methods. Also, the results showed that IG-SFSM has less limitations than the other numerical methods such as IGA and classic FSM.