The present invention is directed to a dual sided incremental sheet forming apparatus and method for incrementally forming sheet materials such as sheet metal by utilizing opposed primary and secondary forming tool assemblies and a sheet feeding assembly. The primary forming tool assembly includes a rigid tool and the secondary forming tool assembly includes a compressible and resilient backing layer having either a cylindrical or flat configuration. The sheet feeding assembly positions the sheet material between the two forming tools. The rigid tool applies force to one surface of the sheet material while the resilient backing tool applies counter force to the opposite surface of the work piece as it supports the work piece. This dual sided process localizes the forces on the sheet material so that stresses are advantageously controlled to produce accurately formed asymmetric shapes, without the need for expensive dies. The use of a rigid tool with an opposed resilient backing tool both having linear independent motion also avoids potential wrinkling and tearing of the resulting work piece and enables the formation of numerous, highly detained asymmetric products.