Quantitative assessment of myocardial function is a valuable tool for clinical applications and physiological studies. This assessment can be acquired using phase based motion sensitive magnetic resonance imaging (MRI) techniques. In this thesis, the accuracy of these phase based motion sensitive MRI techniques is investigated, and modifications in acquisition and post-processing are proposed. The strain rate of the myocardium can be used to evaluate the myocardial function. However, the estimation of strain rate from the velocity data acquired with phase-contrast MRI (PC-MRI) is sensitive to noise. Estimation using normalized convolution showed, however, to reduce this sensitivity to noise and to minimize the influence of non-myocardial tissue which could impair the result. Strain of the myocardium is another measure to assess myocardial function. Strain can be estimated from the myocardial displacement acquired with displacement encoding with stimulated echo (DENSE). DENSE acquisition can be realized with several different encoding strategies. The choice of encoding scheme may make the acquisition more or less sensitive to different sources of error. Two potential sources of errors in DENSE acquisition are the influence of the FID and of the off-resonance effects. Their influence on DENSE were investigated to determine suitable encoding strategies to reduce their influence and thereby improve the measurement accuracy acquired. The quality of the DENSE measurement is not only dependent on the accuracy, but also the precision of the measurement. The precision is affected by the SNR and thereby depends on flip angle strategies, magnetic field strength and spatial variation of the receiver coil sensitivity. A mutual comparison of their influence on SNR in DENSE was therefore performed and could serve as a guideline to optimize parameters for specific applications. The acquisition time is often an important factor, especially in clinical applications where it affects potential patient discomfort and patient through-put. A multiple-slice DENSE acquisition was therefore presented, which allows the acquisition of strain values according to the 16-segment cardiac model within a single breath-hold, instead of the conventional three breath-holds. The DENSE technique can also be adapted toward comprehensive evaluation of the heart in the form of full three-dimensional three-directional acquisition of the displacement. To estimate the full strain tensor from these data, a novel post-processing technique using a polynomial was investigated. The method yielded accurate results on an analytical model and \textit{in-vivo} strains obtained agreed with previously reported myocardial strains in normal volunteers.