A shape sensor is used to determine the shape configuration of a flexible substrate. The shape sensor includes a matrix of coils with a first subset of coils and a second subset of coils; and a controller coupled to the matrix of coils, wherein the controller is configured to generate and transmit an excitation signal to the first subset of coils and measure, on the second subset of coils, an induced signal, and wherein, the controller is configured to determine a spatial configuration of the second subset of coils relative to the first subset of coils based on the induced signal. The shape sensor may be incorporated into a flexible display system so as to determine the degree or state of flexing of the flexible display system.