Tailoring composite materials by fibers of spatially varying orientation angles has been realized with the advent of automated tow-placing machine. In order to use these variable stiffness composite materials as structural components, their responses to multiple external loads should be investigated. In this study, a truncated composite conical shell structure subjected to inflating pressure and surface shear traction force is considered. A mathematical model that predicts strain and stress distributions on the conical shell is developed. Based on the model, numerical examples are given for various fiber paths defined on the truncated conical shell that is subjected to inflating pressure and spatially varying shear traction force on the inner and outer surfaces, respectively. Numerical examples show that, under these external loads, the meridional strain and stress components are very sensitive to the type of fiber path definitions and value of semi-vertex angle of the cone. Boundary conditions have, also, shown remarkable effects on strain and stress distributions. To verify the adequacy of the mathematical model, the truncated composite conical shell of variable stiffness is simulated using finite element based ABAQUS commercial software. The numerical results obtained through the developed mathematical model and ABAQUS simulations show good agreement. (C) 2016 Elsevier Ltd. All rights reserved.