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Definition of inflexible : 1. Firm in will or purpose; not to be turned, changed, or altered; resolute; determined; unyieding; inexorable; stubborn.
2. Incapable of change; unalterable; immutable.
3. Not capable of being bent; stiff; rigid; firm; unyielding.

Synonyms:

tough, rock-hard, self-willed, pat, hardcore, rock-ribbed, unchanging, fixed, resolved, narrow, hardened, hardline, determined, impenetrable, unchangeable, stiffened, pigheaded, unadaptable, taut, intransigent, set, contumacious, ironclad, incommutable, indomitable, perverse, hard-and-fast, conservative, self-opinionated, persistent, inalterable, resist, fossilized, remorseless, semirigid, adamantine, iron, muscle-bound, opinionated, inexorable, bloody-minded, stalwart, unshakable, invariable, heady, implacable, incompliant, die-hard, stand-up, irreversible, final, sturdy, ossified, constant, immutable, headstrong, unrelenting, willful, flinty, hardy, refractory, closed, brassbound, unconquerable, for good, unvarying, cast-iron, bullheaded, hard, packed, stout, granitic, solid, unflinching, inconvincible, flexible, decided, whatever happens, dogged, hard-line, narrow-minded, fossilised, hard core, intractable, uncompliant

immovable, firm, unalterable, stiff

demanding, rigid, austere, fundamental, gruff, rigorous, brusque, dry, uncompromising, precise, curt, piquant, correct, brisk, chilly, obstinate, icy, stiff-necked, bleak, obdurate, disciplined, cutting, spare, stringent, hidebound, blunt, caustic, censorious, lean, cool, tart, exacting, basic, acute, sharp, ascetic, acerbic, imperial, raw, astringent, prudish, meticulous, severe, frosty, Spartan, Draconian, harsh, acrimonious, unbending, intolerant, puritanical, oppressive, keen, critical, authoritarian, short, abrupt, strict, stern, relentless, stark, intense, crisp, grim, strait-laced, dour

contrary, bovine, pertinacious, mulish, brass-bound, bigoted, resolute, inelastic, stubborn, tenacious, unbendable, unyielding, bull-headed, hardheaded, hard-nosed, adamant, pig-headed

Usage examples:

• He foresaw that his lot would be one of comparative exile, and he accepted it with a calm and inflexible resolution. - "His Sombre Rivals", E. P. Roe.
• The knowledge of a scholar, the courage of a hero, and the virtue of a Stoic, will be admired; but if the knowledge be accompanied with arrogance, the courage with ferocity, and the virtue with inflexible severity, the man will never be loved. - "Letters to His Son, 1749", The Earl of Chesterfield.
• She would be inflexible- he knew her. - "The Matador of the Five Towns and Other Stories", Arnold Bennett.