In this work, we study the influence of the boundary conditions in the stress distribution and the first ply failure of a commercially available multilayer composite pipe using a finite element model. An ASTM D2290 standard test was performed to determine the ultimate tensile strength and burst pressure. Also, an ASTM D3039 tension test performed on a longitudinal strip of the pipe was used to evaluate the elastic constants. We compared the experimental results with the numerical model to validate the material parameters used in the approximation. Hoop and axial stresses were obtained for three different boundary conditions: open, fixed and closed ends. Different failure criteria were considered to evaluate the first ply failure, and a comparison of failure criteria and boundary conditions was made. The apparent stress using finite elements corresponds to 82.31MPa, the error between the experimental test and the numerical model is 1.06%. For a nominal pressure of 5.17MPa, the composite laminate layer exhibits a hoop stress of 62MPa for the stress. For open-end pipes, first ply failure is reached at 10.48MPa under Hoffman criterion.