Heart failure (HF) is one of the leading causes of death worldwide. HF is associated with substantial microstructural remodeling, which is linked to changes in left ventricular geometry and impaired cardiac function. The role of myocardial remodeling in altering the mechanics of failing hearts remains unclear. Structurally based constitutive modeling provides an approach to improve understanding of the relationship between biomechanical function and tissue organization in cardiac muscle during HF. In this study, we used cardiac magnetic resonance imaging and extended-volume confocal microscopy to quantify the remodeling of left ventricular geometry and myocardial microstructure of healthy and spontaneously hypertensive rat hearts at the ages of 12 and 24 months. Passive cardiac mechanical function was characterized using left ventricular pressure-volume compliance measurements. We have developed a, to our knowledge, new structurally based biomechanical constitutive equation built on parameters quantified directly from collagen distributions observed in confocal images of the myocardium. Three-dimensional left ventricular finite element models were constructed from subject-specific in vivo magnetic resonance imaging data. The structurally based constitutive equation was integrated into geometrically subject-specific finite element models of the hearts and used to investigate the underlying mechanisms of ventricular dysfunction during HF. Using a single pair of material parameters for all hearts, we were able to produce compliance curves that reproduced all of the experimental compliance measurements. The value of this study is not limited to reproducing the mechanical behavior of healthy and diseased hearts, but it also provides important insights into the structure-function relationship of diseased myocardium that will help pave the way toward more effective treatments for HF.