In this work an attempt has been made to develop theories for finite element static and dynamic stress analysis tailored for use with composite layered plates and shells in this way it was hoped to provide accurate values of the stresses particularly transverse shear stresses through the thickness, and to perform accurate natural frequency analysis by including non-linear effects such as centrifugal stiffening. Initial derivations were based upon first order facet shell element analysis and first order curved shell element analysis. Subsequently, derivations were produced for higher order element analysis. A programming package has been developed based upon the above derivations, and containing a banded solver as well as a frontal solver, capable of analysing structures build up from uniform or variable thickness layers and with a multiple number of layers having constant or variable dimension. Results obtained with the aid of the present package have been compared with results derived from experimental work as well as with results derived from available analytical solutions. Investigations have been carried out for existing compressor blades, made of isotropic material and layered composite material, respectively. The results obtained from the package have been compared with available experimental results produced by RR or carried out at Cranfield. It has been shown that the above mentioned derivations produce comparable results and the package has proved to be reliable and accurate.