This paper reports on the rapid fabrication of radially-aligned, three-dimensional conical struc- tures by electrospinning. Three different polymers, Polyvinylpyrrolidone, Polystyrene and Polyacrylonitrile were used to electrospin the cones. These cone structures are spreading out from a vertical conductive pillar, which can be arbitrarily placed on specific part of the collector. The lower part of the cone is clearly defined on the collec- tor, and the cone has a relatively uniform radius around the pillar. The cones are constituted of fibers that are ra- dially aligned towards the top of the pillar, but there is no apex and the fibers fall flat on the top of the pillar surface. A parametric study has been performed to investigate the effects of the pillar morphology (height and thickness) and the electrospinning parameters (applied voltage and working distance) on the overall shape and size of the cone structure, as well as the fiber alignment. The pillar morphology influences directly the cone diameter and height. The electrospinning parameters have little effect on the cone structure. The formation mechanism has been identified to be related to the shape of the electric field, which has been systematically simulated to understand the effect of the electric field lines on the final dimensions of the cone structure.