Field applications of existing sensing solutions to structural health monitoring (SHM) of civil structures are limited. This is due to economical and/or technical challenges in deploying existing sensing solutions to monitor geometrically large systems. To realize the full potential of SHM solutions, it is imperative to develop scalable cost-effective sensing strategies. We present a novel sensor network specifically designed for strain sensing over large surfaces. The network consists of soft elastomeric capacitors (SECs) deployed in an array form. Each SEC acts as a surface strain gage transducing local strain into changes in capacitance. Results show that the sensor network can track strain history above levels of 25 με using an inexpensive off-the-shelf data acquisition system. Tests at large strains show that the sensor's sensitivity is almost linear over strain levels of 0-20%. We demonstrate that it is possible to reconstruct deflection shapes for a simply supported beam subjected to quasi-static loads, with accuracy comparable to resistive strain gages.