word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
1650s, formerly also elastick, coined in French (1650s) as a scientific term to describe gases, "having the property of recovering its former volume after compression," from Modern Latin elasticus, from Greek elastos "ductile, flexible," related to elaunein "to strike, beat out," which is of uncertain origin; according to Watkins from an extended form of the PIE base *ele- "to go."
Applied to solids from 1670s, "having the power of returning to the form from which it is bent, etc., as soon as the applied force is removed." Figurative use by 1859. The noun meaning "piece of elastic material," originally a cord or string woven with rubber, is from 1847, American English.
<a href="https://www.etymonline.com/word/inelastic">Etymology of inelastic by etymonline</a>
Harper, D. (n.d.). Etymology of inelastic. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/inelastic