The impact of fluid drops on solid surfaces is a fundamental fluid dynamics phenomenon with applications in many fields such as: inkjet based bioprinting of cells, tissues and organs, production of capsules, beads and spherical particles. Existing studies on this subject have focused on spherical Newtonian drops, which have little or no effect in understanding this flow phenomenon in industrial conditions where the drops are largely non-Newtonian and non-spherical. Hence, both shape and rheological effects on the drop spreading dynamics remains mostly unexplored. This work employs a mixed approach of experiments and multiphase three-dimensional numerical simulations to extend the work reported by Luu and Forterre (2009) by highlighting the intrinsic role of the aspect ratio of viscoplastic drops when impacting a solid. Spherical, prolate, cylindrical and prismatic drops are considered. The results show that, with negligible capillary effects, the impacting (kinetic) energy of the drop is dissipated through viscoplastic effects during the spreading on the surface, giving rise to three flow (spreading) regimes: (I) inertia-viscous; (II) inertia-plastic; and (III) mixed inertia-viscoplastic. These regimes are deeply affected by the initial aspect ratio of the drops, which in turn reveals the potential to control spreading with the drop shapes. The physical mechanisms driving the considered phenomenon are highlighted by energy budget analyses. With the proposed new scaling laws, the results obtained are robustly summarised in a two-dimensional diagram linking the drop’s maximum spreading to the different spreading regimes through a single dimensionless parameter named the impact number.