An analytical model was developed using the first-order laminated shell theory to determine stress and strain distributions within a composite pipe joint under combined torsional and tensile loading. Due to the axisymmetric nature of torsional and tensile loads about the pipe's central axis, a one-dimensional model was sufficient to simulate the system response. In this developed model, a three-component joint system consisting of coupling, adhesive, and pipe was used to model different types of composite pipe joints, such as adhesive-bonded socket joints, butt-and-strap joints, and heat-activated coupling joints. Good correlations were found when comparing results from both the developed model and the finite element model, including adhesive peel stress and shear stress distributions.