As far as design of composite structures is concerned, it is important that we are able to accurately determine the failure modes and damage progression of structures made of composite materials. This will in turn, aid structural designers to develop reliable and safe designs which will exploit the advantages offered by composite materials. With the development of numerical analysis strategies towards non-linear progressive failure algorithms and the increase in computing capacity, it has now become possible to replace the existing experimental data with numerical results. Verified numerical models offer a practical method for exploring parametric study. Hence, it is essential to devise a reliable progressive damage scheme in order to predict the damage propagation in composite laminated structures using efficient computational tools such as the finite strip method. In this thesis, a new finite strip method, for non-linear stress analysis based on the tangential stiffness matrix has been developed using the new concept of polynomial and spline-type finite strip elements, with Mindlin and Reissner plate-bending theories for composite plates and shells. A progressive damage methodology and algorithm for composite laminates was successfully developed for the new finite strip methods using stress-based failure criteria. A finite strip analysis programming package which is capable of performing nonlinear progressive damage analysis for composite plates and facetted shells, has also been developed with Mindlin and Reissner plate bending elements. Validation of the developed finite strip package has been successfully carried out by comparing the results with corresponding results obtained with the finite element analysis using ABAQUS and with some published experimental results. Good comparison with the finite element results and experimental results were observed through various test cases, confirming the accuracy and reliability of the new derivations and the programming package.