Highlights• A nonlinear buckling model is established for composite cylindrical shells with hygrothermal-electro-elastic coupled loading fields.• The accuracy of the proposed model is improved by introducing non-uniform pre-buckling effects.• Nonlinear buckling solutions with axisymmetric and non-axisymmetric buckling solutions are derived.• Critical buckling stresses/pressures and corresponding analytical buckling modes are presented.• Parameter analyses on the critical buckling loads and buckling modes are established.