Myocardium resists the inflow of blood during diastole through stretch-dependent generation of passive tension. Earlier we proposed that this tension is mainly due to collagen stiffness at degrees of stretch corresponding to sarcomere lengths (SLS) > or = 2.2 microns, but at shorter lengths, is principally determined by the giant sarcomere protein titin. Myocardial passive force consists of stretch-velocity-sensitive (viscous/viscoelastic) and velocity-insensitive (elastic) components; these force components are seen also in isolated cardiac myofibrils or skinned cells devoid of collagen. Here we examine the cellular/myofibrillar origins of passive force and describe the contribution of titin, or interactions involving titin, to individual passive-force components. We construct force-extension relationships for the four distinct elastic regions of cardiac titin, using results of in situ titin segment-extension studies and force measurements on isolated cardiac myofibrils. Then, we compare these relationships with those calculated for each region with the wormlike-chain (WLC) model of entropic polymer elasticity. Parameters used in the WLC calculations were determined experimentally by single-molecule atomic force-microscopy measurements on engineered titin domains. The WLC modelling faithfully predicts the steady-state-force vs. extension behavior of all cardiac-titin segments over much of the physiological SL range. Thus, the elastic-force component of cardiac myofibrils can be described in terms of the entropic-spring properties of titin segments. In contrast, entropic elasticity cannot account for the passive-force decay of cardiac myofibrils following quick stretch (stress relaxation). Instead, slower (viscoelastic) components of stress relaxation could be simulated by using a Monte-Carlo approach, in which unfolding of a few immunoglobulin domains per titin molecule explains the force decay. Fast components of stress relaxation (viscous drag) result mainly from interaction between actin and titin filaments; actin extraction of cardiac sarcomeres by gelsolin immediately suppressed the quickly decaying force transients. The combined results reveal the sources of velocity sensitive and insensitive force components of cardiomyofibrils stretched in diastole.