In this dissertation a novel method has been proposed for solution of time harmonic vibration and static problems of laminated beams and plates. In the method a series of fundamental exponential functions have been used to satisfy the governing static/dynamic equations in each lamina. Compatibility between the layers, along the beam, is rigorously satisfied through defining a characteristic problem. The boundary conditions at the two ends of the beam are satisfied by a particular discrete transformation. The results have been compared with available solutions for some benchmark problems. Excellent agreement is observed between the solutions. Some more problems have been solved as new benchmarks for further studies.