During the morphogenetic process of cardiac looping, the initially straight cardiac tube bends and twists into a curved tube. The biophysical mechanisms that drive looping remain unknown, but the process clearly involves mechanical forces. Hence, it is important to determine mechanical properties of the early heart, which is a muscle-wrapped tube consisting primarily of a thin outer layer of myocardium surrounding a thick extracellular matrix compartment known as cardiac jelly. In this work, we used microindentation experiments and finite element modeling, combined with an inverse computational method, to determine constitutive relations for the myocardium and cardiac jelly at the outer curvature of stage 12 chick hearts. Material coefficients for exponential strain-energy density functions were found by fitting force-displacement and surface displacement data near the indenter Residual stress in the myocardium also was estimated. These results should be useful for computational models of the looping heart.