This paper presents a new design architecture for mechanically flexible light-emitting diode (LED) signage modules for applications in digital advertising on curved surfaces. The new design comprises an array of commonly used rigid printed circuit boards (PCBs) but of smaller size with some spacing between them, which is encapsulated by a flexible substrate or potting material, instead of a large single rigid PCB in the entire LED module as in the case of conventional LED signage modules. Commonly used through-hole type RGB LEDs are considered. To demonstrate the design, manufacturing, and mechanical flexibility of the design, a prototype LED signage module with a typical industry standard size of 304 mmx304 mmx10 mm was designed and fabricated. Experimental testing and finite element simulations were conducted to analyze mechanical flexibility and internal stresses in the module. The results demonstrate that the new design provides flexible LED modules, without altering the conventional LED control system. It is shown that maximum stress occurs in the spacing between the PCBs and is small even for large module deflection. As the curvature of module deflection was decreased, the maximum stress increased, indicating as an important design parameter for the module deflection. The proposed design architecture will enable both indoor and outdoor digital advertising using billboards on a wide range of curved surfaces.