The Collaborative International Dictionary of English v.0.48:

Inflexibility \In*flex"i*bil"i*ty\, n. [Cf. F.
   inflexibilit['e].]
   The quality or state of being inflexible, or not capable of
   being bent or changed; unyielding stiffness; inflexibleness;
   rigidity; firmness of will or purpose; unbending pertinacity;
   steadfastness; resoluteness; unchangeableness; obstinacy.
   [1913 Webster]

         The inflexibility of mechanism.          --A. Baxter.
   [1913 Webster]

         That grave inflexibility of soul.        --Churchill.
   [1913 Webster]

         The purity and inflexibility of their faith. --T.
                                                  Warton.
   [1913 Webster]

WordNet (r) 3.0 (2006):

inflexibility
    n 1: a lack of physical flexibility [syn: inflexibility,
         inflexibleness] [ant: flexibility, flexibleness]
    2: the quality of being rigid and rigorously severe [syn:
       inflexibility, rigidity, rigidness] [ant:
       flexibility, flexibleness]

Moby Thesaurus II by Grady Ward, 1.0:

95 Moby Thesaurus words for "inflexibility":
   act of God, adamantness, certainty, concentration, constancy,
   dourness, fate, fatefulness, firmness, firmness of mind, fixedness,
   flintiness, force majeure, fundamentalism, grimness,
   hard-bittenness, hard-nosedness, hardness, immobility,
   immobilization, immovability, immovableness, immutability,
   implacability, impliability, indefeasibility, inductility,
   inelasticity, ineluctability, inertia, inescapableness,
   inevasibleness, inevitability, inevitable accident, inevitableness,
   inexorability, inextensibility, inextricability, intractability,
   intransigeance, intransigence, intransigency, intransigentism,
   irreconcilability, irremovability, irresilience, irresiliency,
   irrevocability, loyalty, necessity, obduracy, obdurateness,
   obstinacy, orthodoxy, precisianism, predetermination, purism,
   puritanism, relentlessness, rigidity, rigidness, rigor, rigorism,
   rigorousness, settledness, solidity, staunchness, steadfastness,
   steadiness, steeliness, sternness, stiff temper, stiffness,
   stubbornness, sureness, toughness, trueness, unalterability,
   unavoidable casualty, unavoidableness, unbendingness,
   unchangeability, uncompromisingness, uncontrollability,
   undeflectability, ungivingness, unlimberness, unmalleability,
   unmovability, unpliability, unpreventability, unrelentingness,
   unyieldingness, vis inertiae, vis major