Dome curvatures of pressure vessels often sustain highest level of stresses when subjected to various loading conditions. This research is aimed at investigating the effect of dome geometrical shape (hemispherical, torispherical, and ellipsoidal domes) on mechanical deformation and crack length of laminated woven reinforced polymer (GRP) composite pressure vessels under low-velocity impact (LVI) (case one) or combination of LVI and internal pressure (case two). The study is based on finite element (FE) simulations with laboratory-based experimental validation studies. It was observed that the maximum vertical displacements (U1 *) and crack length along the diameter of deformation (a) are both of lower magnitude in case one. Damage intensity and fracture differ for different combinations of loading. Only matrix breakage and debonding occurs in case one and fiber breakage occurs in case two. The dome geometric shapes used in this study were found to be invariant to both damage intensity and failure modes. Irrespective of the type of load applied, the magnitude of U1 * and crack length correlate with dome geometric shape as the maximum and the minimum U1 * occur in torispherical and hemispherical domes, respectively. The maximum and the minimum crack lengths also take place in torispherical and hemispherical domes, respectively. © 2018 Politechnika Wroc�awska