Feasibility of applying compressive sensing (CS) to ultrasound radio-frequency (RF) data to produce elastography is investigated. The research also compares the performance of various CS frameworks associated with three common model bases (Fourier transform, discrete cosine transform (DCT), and wave atom (WA)) and two reconstruction algorithms (ℓ1 minimization and block sparse Bayesian learning (BSBL)) using the quality of B-mode images and elastograms from the RF data subsampled and reconstructed by each framework. Results suggest that CS reconstruction adopting BSBL algorithm with DCT model basis can yield the best results for all the measures tested, and the maximum data reduction rate for producing readily discernable elastograms is around 60%.