A block wall system comprising a framework having a perimeter, an intermediate vertical mullion, and an intermediate horizontal mullion with the blocks retained therein using flexible flanges. The intermediate vertical mullion and the intermediate horizontal mullion define one or more cavities within the framework. A block has a top, a bottom, a front face, a back face, and a pair of narrow faces. One or more detents are defined within each narrow face. Next, a flange is anchored within the intermediate vertical mullion, wherein the flange flexes and thereafter retracts to embed itself into the detent of the block when the block is inserted into the cavity such that the block is retained within the framework, thereby eliminating the need to use a fastener directly into or against the block to secure the block within the framework.