A myocardial infarction can cause irreversible damage to the heart muscle. A promising approach for the treatment of myocardial infarction and prevention of severe complications is the application of cardiac patches or epicardial restraint devices. The challenge for the fabrication of cardiac patches is the replication of the fibrillar structure of the myocardium, in particular its anisotropy and local elasticity. In this study, we developed a chitosan–gelatin–guar gum-based biomaterial ink that was fabricated using 3D printing to create patterned anisotropic membranes. The experimental results were then used to develop a numerical model able to predict the elastic properties of additional geometries with tunable elasticity that could easily match the mechanical properties of the heart tissue (particularly the myocardium).