The protein titin functions as a mechanical spring conferring passive elasticity to muscle. Force spectroscopy studies have shown that titin exhibits several regimes of elasticity. Disordered segments bring about a soft, entropic spring-type elasticity; secondary structures of titin's immunoglobulin-like (Ig-) and fibronectin type III-like (FN-III) domains provide a stiff elasticity. In this study, we demonstrate a third type of elasticity due to tertiary structure and involving domain-domain interaction and reorganization along the titin chain. Through 870 ns of molecular dynamics simulations involving 29,000-635,000 atom systems, the mechanical properties of a six-Ig domain segment of titin (I65-I70), for which a crystallographic structure is available, are probed. The results reveal a soft tertiary structure elasticity. A remarkably accurate statistical mechanical description for this elasticity is derived and applied. Simulations also studied the stiff, secondary structure elasticity of the I65-I70 chain due to the unraveling of its domains and revealed how force propagates along the chain during the secondary structure elasticity response.