The Collaborative International Dictionary of English v.0.48:

Rigid \Rig"id\, a. [L. rigidus, fr. rigere to be stiff or numb:
   cf. F. rigide. Cf. Rigor. ]
   1. Firm; stiff; unyielding; not pliant; not flexible.
      [1913 Webster]

            Upright beams innumerable
            Of rigid spears.                      --Milton.
      [1913 Webster]

   2. Hence, not lax or indulgent; severe; inflexible; strict;
      as, a rigid father or master; rigid discipline; rigid
      criticism; a rigid sentence.
      [1913 Webster]

            The more rigid order of principles in religion and
            government.                           --Hawthorne.
      [1913 Webster]

   Syn: Stiff; unpliant; inflexible; unyielding; strict; exact;
        severe; austere; stern; rigorous; unmitigated.
        [1913 Webster]

WordNet (r) 3.0 (2006):

rigid
    adj 1: incapable of or resistant to bending; "a rigid strip of
           metal"; "a table made of rigid plastic"; "a palace
           guardsman stiff as a poker"; "stiff hair"; "a stiff neck"
           [syn: rigid, stiff]
    2: incapable of compromise or flexibility [syn: rigid,
       strict]
    3: incapable of adapting or changing to meet circumstances; "a
       rigid disciplinarian"; "an inflexible law"; "an unbending
       will to dominate" [syn: inflexible, rigid, unbending]
    4: designating an airship or dirigible having a form maintained
       by a stiff unyielding frame or structure [ant: nonrigid]
    5: fixed and unmoving; "with eyes set in a fixed glassy stare";
       "his bearded face already has a set hollow look"- Connor
       Cruise O'Brien; "a face rigid with pain" [syn: fixed,
       set, rigid]

Moby Thesaurus II by Grady Ward, 1.0:

204 Moby Thesaurus words for "rigid":
   abiding, accurate, adamant, adamantine, at a standstill, attentive,
   austere, buckram, careful, cast-iron, changeless, close,
   conscientious, constant, continuing, correct, critical, delicate,
   demanding, detailed, determined, direct, dogged, dour, draconian,
   durable, enduring, even, exact, exacting, exigent, express,
   exquisite, faithful, fine, finical, finicking, finicky, firm,
   firm as Gibraltar, fixed, flinty, frozen, fundamentalist, fussy,
   grim, hard, hard and fast, hard-core, hard-line, harsh, headstrong,
   hidebound, immobile, immotile, immotive, immovable, immutable,
   implacable, impliable, in buckram, inelastic, inerrable, inerrant,
   inexorable, infallible, inflexible, infrangible, intact,
   intransigent, inviolate, iron, ironbound, ironclad, ironhanded,
   irreconcilable, irremovable, lasting, literal, made of iron,
   mathematical, meticulous, micrometrically precise, microscopic,
   minute, mulish, muscle-bound, narrow, nice, obdurate, obstinate,
   orthodox, painstaking, particular, pat, permanent, perpetual,
   persevering, persistent, pigheaded, pinpoint, pokerlike, precise,
   precisianistic, precisionistic, prim, procrustean, punctilious,
   punctual, purist, puristic, puritan, puritanic, quiescent,
   ramrodlike, refined, relentless, religious, religiously exact,
   remaining, renitent, resolute, resolved, rigorist, rigoristic,
   rigorous, rock-ribbed, rockbound, rodlike, scientific,
   scientifically exact, scrupulous, scrutinizing, set, severe,
   single-minded, solid, sound, square, stable, standpat, starch,
   starched, starchy, static, stationary, staunch, staying, steadfast,
   steely, stern, stiff, stiff as buckram, stilted, stout,
   straightlaced, strait-laced, straitlaced, strict, stringent,
   strong, stubborn, sturdy, subtle, sustained, taut, tenacious,
   tense, thorough, tight, torpid, tough, unadaptable, unaffected,
   unalterable, unaltered, unbending, unbreakable, unchangeable,
   unchanged, unchanging, unchecked, uncompliant, uncompromising,
   undestroyed, undeviating, unerring, unfading, unfailing,
   unflexible, ungiving, unmovable, unmoved, unmoving, unqualified,
   unrelaxed, unrelenting, unshifting, unswerving, unvaried,
   unvarying, unwavering, unyielding, virgate