This paper presents the development of a mathematical model based on curved beam theory of composite pipes with irregular shapes under diametral loading. The analytical solution was validated through finite element models of the same pipe shapes under similar loading conditions. Four shapes (circular, elliptical, rectangular, and egg shaped pipes) were considered in this study. The analytical and finite element results were used to estimate the shape factor defined by the ratio of the maximum tangential stress of an irregular shape over the maximum tangential stress for a circular pipe. Comparison of the load-deflection curves for the four different shapes revealed that the egg pipe is the stiffest among the rest of the pipes while the square shape is the most flexible one. The analytical solution and finite element results were used to determine the shape factor for the four pipe shapes taking into account the circular pipe as the base shape. Both results were in good agreement and can be used as design guidelines for the irregular shapes without resorting to the conduct of any further testing.