The Collaborative International Dictionary of English v.0.48:

Rigidity \Ri*gid"i*ty\, n. [L. rigiditas: cf. F. rigidit['e].
   See Rigid.]
   1. The quality or state of being rigid; want of pliability;
      the quality of resisting change of form; the amount of
      resistance with which a body opposes change of form; --
      opposed to flexibility, ductility, malleability, and
      softness.
      [1913 Webster]

   2. Stiffness of appearance or manner; want of ease or
      elegance. --Sir H. Wotton.
      [1913 Webster]

   3. Severity; rigor. [Obs. orR.] --Bp. Burnet.
      [1913 Webster]

   Syn: Stiffness; rigidness; inflexibility.
        [1913 Webster]

WordNet (r) 3.0 (2006):

rigidity
    n 1: the physical property of being stiff and resisting bending
         [syn: rigidity, rigidness]
    2: the quality of being rigid and rigorously severe [syn:
       inflexibility, rigidity, rigidness] [ant:
       flexibility, flexibleness]