New elastographic techniques such as poroelastography and viscoelasticity imaging aim at imaging the temporal mechanical behavior of tissues. These techniques usually involve the use of curve fitting methods as applied to noisy data to estimate new elastographic parameters. As of today, however, image quality performance of these new elastographic imaging techniques is still largely unknown due to a paucity of data and the lack of systematic studies that analyze performance limitations of estimators suitable for these novel applications. Furthermore, current elastographic implementations of poroelasticity and viscoelasticity imaging methods are in general too slow and not optimized for clinical applications. In this paper, we propose a new elastographic time constant (TC) estimator, which is based on the use of the Least Square Error (LSE) curve-fitting method and the Levenberg-Marquardt (LM) optimization rule as applied to noisy elastographic data obtained from a tissue under creep compression. The estimator's performance is analyzed using simulations and quantified in terms of accuracy, precision, sensitivity, signal-to-noise ratio (SNR) and speed. Experiments are performed as a proof of principle of the technical applicability of the new estimator on real experimental data. The results of this study demonstrate that the new elastographic estimator described in this thesis can produce highly accurate, sensitive and precise time constant estimates in real-time and at high SNR. In the future, the use of this estimator could allow real-time imaging of the temporal behavior of complex tissues and provide advances in lymphedema and cancer imaging.