A variable radius sanding block for sanding curved surfaces. The variable radius sanding block includes a base member and a plurality of variably sized radius patches. The base member is sized and proportioned to allow radius patches of varying size to be inserted, such that each of the radius patches will change the curvature of the sanding block upon insertion. The base member also having a folded flexible internal structure and a pair of flexible arms that facilitate insertion of radius patches of varying size. The radius patch includes a pair of grooves that receive the flexible arms of the base member and secure the base member to the radius patch.