Composite cylinders are high-strength containers made from a mixture of fibre glass or carbon fibers and a plastic resin typically epoxy. A lamina is assumed to be homogeneous and the mechanical behavior is characterized by a set of equivalent or effective moduli and strength properties. In the phenomenological approach, the lamina properties are determined experimentally by conducting tests on a single lamina or a laminate. Once the mechanical properties of the ply are known the initial failure of the ply within a laminate or structure can be predicted by applying an appropriate failure criterion. Failure types are dependent on loading, stacking sequence, and specimen geometry. There are many proposed theories to predict the one-set of failures. Most of failure criteria are based on the stress state in a lamina. The present work aims to determine the effect of diameter-to-thickness ratio 'S' with respect to failure pressure of a four layers, introduction of hoop layers at ends on four layered cylinder and introduction of hoop layers at middle of six layered angle-ply laminated cylinder which is analyzed by using Finite Element software ANSYS. The variation of failure pressure with respect to fiber angles was also presented in this work.