This paper presents the effect of oblique impact angle on low velocity transient dynamic responses of delaminated composite pretwisted shallow conical shells. An eight-noded isoparametric quadratic plate bending element is employed in the finite element formulation incorporating rotary inertia and effects of transverse shear deformation based on Mindlin’s theory. The modified Hertzian contact law which accounts for permanent indentation is utilized to compute the contact force, and the time-dependent equations are solved by Newmark’s time integration scheme. A comparative study is carried out on torsion stiff, cross-ply, and bending stiff laminates to investigate the effects of triggering parameters like angle of twist, plate displacement, striker’s velocity, and displacement for graphite-epoxy composite laminate subjected to low velocity oblique impact at the center.