Methods and apparatuses for compacting soil and granular materials. The soil compaction apparatuses include an arrangement of diametric expansion elements that, in their expanded state, form a larger compaction surface. In another embodiment, a compaction chamber can be provided with diametric restriction elements and a flow-through passage in the upper portion of the chamber exterior of a drive shaft. The diametric expansion or restriction elements can be fabricated from, for example, individual chains, cables, or wire rope, or a lattice of vertically and horizontally connected chains, cables, or wire rope. Embodiments of the soil compaction apparatus include, but are not limited to, closed-ended driving shafts, open-ended driving shafts, flow-through passages, no flow-through passages, removable rings for holding the diametric expansion/restriction elements, and any combinations thereof.