The invention discloses methods of forming strained channel regions on FinFET devices. One illustrative method disclosed herein includes, among other things, removing at least a portion of a vertical height of portions of an overall fin structure that are not covered by a gate structure so as to result in the definition of a fin cavity in a layer of insulating material and the definition of a remaining portion of the overall fin structure that is positioned under the gate structure, wherein the remaining portion comprises a channel portion and a lower portion located under the channel portion. The method continues with the formation of a first semiconductor material within at least the fin cavity and the formation of a second semiconductor material on the first semiconductor material and on exposed edges of the channel portion.