A conveyor belt having rodless, living hinges and a method for making such a belt. One version of the belt has spaced apart belt modules joined by tension members spanning the gaps between consecutive modules. The tension members bend in the gaps to allow the belt to articulate. Resilient fillers encapsulate the tension members and, together with top surfaces of the modules, form a generally continuous article-contacting belt surface. The belt may be made by molding the rigid belt modules and the resilient fillers onto an arrangement of elongated tension members.