An imaging system that can detect and predict the propensity of an atherosclerotic plaque to rupture would reduce stroke. Radial and circumferential strain elastograms can reveal vulnerable regions within the fibrous cap. Circumferential stress imaging could predict the propensity of rupture. However, circumferential stress imaging demands either accurate knowledge of the geometric location of the fibrous cap or high quality strain information. We corroborated this hypothesis by performing studies on simulated vessel phantoms. More precisely, we computed stress elastograms with (1) precise knowledge of the fibrous cap, (2) no knowledge of the fibrous cap, (3) imprecise knowledge of the fibrous cap. We computed stress elastograms with accuracy of 8%, 15%, and 23% from high precision axial and lateral strain elastograms (i.e., 25 dB SNR) when precise, imprecise, and no geometric information was included the stress recovery method. The stress recovery method produced erroneous elastograms at lower noise level (i.e., 15 dB SNR), when no geometric information was included. Similarly, it produced elastograms with accuracy of 13% and 30% when precise and imprecise geometric information was included. The stress imaging method described in this paper performs well enough to warrant further studies with phantoms and ex-vivo samples.