Methods of braiding using a braiding mechanism are described. The braiding mechanism includes a circular array of filament engagement elements, a mandrel extending from the center of the circular array, a plurality of actuators disposed operably about the circular array, and a rotating mechanism adapted to rotate one or more filaments. The circular array of filament engagement elements and the plurality of actuators are configured to move relative to one another. The plurality of filaments are loaded onto the mandrel and extend radially toward and contact the circumferential edge of the circular array of filament engagement elements. The plurality of actuators are operated to engage a first subset of the plurality of filaments and move the engaged filaments in a generally radial direction to a position beyond the circumferential edge of the circular array. The rotating mechanism is operated to move the engaged filaments about the mandrel axis.