Purpose <p>This is the first time that the finite element method is built on the basis of higher-order shear deformation theory to analyze the free vibration and transient response of a sandwichdoubly-curved shallow shell subjected to low-velocity impact loads.</p> Methods <p>The impact load model in this article is described analytically: single spring-mass (S–M) model. The sandwich doubly-curved shallow resting on the visco-Pasternak medium ischaracterized by two stiffness parameters and one damping parameter. A high-precision quadrilateral shell element with four nodes, each of which has eight degrees of freedom, isdeveloped on the basis of Lagrange and <i>C</i>^<i>1</i>-order non-conforming Hermite shape functions to build the stiffness matrix, damping matrix, mass matrix, and force vector of the shell.</p> Results <p>The model’s accuracy and the article’s calculation technique are confirmed numerically by comparison with reputable publications. In addition, the influence of input parameters ofthe sandwich shell and low-velocity impact loads on the dynamic response of the shell is explored.</p> Conclusion <p>The findings derived from this article may be used in the development of military and civilian infrastructure when the structure is exposed to impact forces.</p>