Phase contrast magnetic resonance imaging (MRI) can provide in vivo myocardial velocity field measurements. These data allow densely spaced material points to be tracked throughout the whole heart cycle using, for example, the Fourier tracking algorithm. To process the tracking results for myocardial deformation and strain quantification, we developed a method that is based on fitting the tracking results to an appropriate local deformation model. We further analyzed the accuracy and precision of the method and provided performance predictions for several local models. In order to validate the method and the theoretical performance analysis, we conducted controlled computer simulations and a phantom study. The results agreed well with expectations. Human heart data were also acquired and analyzed, and provided encouraging results. At the signal-to-noise ratio (SNR) level and spatial resolution expected in clinical settings, the study predicts strain quantification accuracy and precision that may allow the technique to become a practical and powerful noninvasive approach for the study of cardiac function, although clinically acceptable data acquisition strategies for three-dimensional (3-D) data are still a challenge.