High energy consumption, excessive data storage and transfer requirements are prevailing issues associated with structural health monitoring (SHM) systems, especially with those employing wireless sensors. Data compression is one of the techniques being explored to mitigate the effects of these issues. Compressive sensing (CS) introduces a means of reproducing a signal with a much less number of samples than the Nyquist's rate, reducing the energy consumption, data storage and transfer cost. This paper explores the applicability of CS for SHM, in particular for damage detection and localization. CS is implemented in a simulated environment to compress SHM data. The reconstructed signal is verified for accuracy using structural response data obtained from a series of tests carried out on a reinforced concrete (RC) slab. Results show that the reconstruction was close, but not exact as a consequence of the noise associated with the responses. However, further analysis using the reconstructed signal provided successful damage detection and localization results, showing that although the reconstruction using CS is not exact, it is sufficient to provide the crucial information of the existence and location of damage.