Deformation and structure of the cardiac wall can be assessed non-invasively by imaging techniques such as magnetic resonance imaging. Understanding the (patho-)physiology that underlies the observed deformation and structure is critical for clinical diagnosis. However, much about the genesis of deformation and structure is unknown. In the present computational model study, we hypothesize that myofibers locally adapt their orientation to achieve minimal fiber-cross fiber shear strain during the cardiac cycle. This hypothesis was tested in a 3D finite element model of left ventricular (LV) mechanics by computation of tissue deformations and subsequent adaptation of initial myofiber orientations towards those in the deformed tissue. As a consequence of adaptation, local tissue peak stress, strain during ejection and stroke work density were all found to increase by at least 10%, as well as to become 50% more homogeneous throughout the wall. Global LV work (peak systolic pressure, stroke volume and stroke work) increased significantly as well (>9%). The model-predicted myofiber orientations were found to be similar to those in experiments. To the best of our knowledge the presented model is the first that is able to simultaneously predict a realistic myocardial structure as well as to account for the experimentally observed homogeneity in local mechanics.