Composite tubes are widely used in automobile and aerospace applications. In engineering practice, composite structures are often subjected to multiple loadings. In addition, the in-situ material and strength properties of composite materials possess unavoidable variations that are random in nature. Such variations affect the response and failure of components made of such composite materials. Reliability engineering has been used as an integral part of the product design and development process in modern industrial practice, to accommodate for such in-situ variations. The present thesis focuses on the study of the first-ply failure of the composite tubes, subjected to combined axial and torsional loadings. Since, in many practical applications, tapered tubes are preferred more often over uniform-diameter tubes, the mechanical behavior and failure of tapered composite tubes are studied with more emphasis in the present work. The first-ply failure envelopes of the filament-wound composite tubes are developed based on the Finite Element Modelling and Analysis. A closed-form analytical solution is developed based on the Classical Laminate Theory, which is used to validate the three-dimensional finite element models of the tapered composite tubes created in ANSYS®. Empirical equations are developed in terms of the radius-to-length and radius-to-thickness ratios, the fiber orientation, and the taper angle to calculate the first-ply failure loadings of the tapered composite tubes. The reliability of the composite tubes is quantified considering the in-situ material properties to be random variables. The reliability-based first-ply failure envelopes of the uniform-diameter and tapered composite tubes are developed based on the Monte Carlo Simulation method.