Old English streccan, from Proto-Germanic *strakjanan (cf. Danish strække, Swedish sträcka, Old Frisian strekka, Old High German strecchan, Middle Low German, Middle Dutch, Old High German, German strecken "to stretch"), perhaps a variant of the root of stark, or else from PIE root *strenk- "tight, narrow; pull tight, twist" (see strain).
Meaning "to extend (the limbs or wings)" is from c.1200; that of "to lay out for burial" is from early 13c. To stretch one's legs "take a walk" is from c.1600. Meaning "to lengthen by force" first recorded late 14c.; figurative sense of "to enlarge beyond proper limits, exaggerate," is from 1550s. Stretch limo first attested 1973. Stretch marks is attested from 1960. Stretcher "canvas frame for carrying the sick or wounded" is first attested 1845.