'saddle-shaped' is a compound in modern English formed from 'saddle' + the past-participial/combining form '-shaped' (from 'shape'). 'saddle' comes from Old English 'sadol' and earlier Proto-Germanic '*sathulaz' meaning 'seat'; 'shape' comes from Old English 'sceapan'/'scapan' meaning 'to form, create'.

'saddle' changed from Old English 'sadol' to Middle English forms like 'sadel' and eventually to modern English 'saddle'. 'shape' evolved from Old English 'sceapan' (to form) through Middle English 'shapen/shape' into modern 'shape'. The compound 'saddle-shaped' appears in modern English by compounding the noun with the participial/adjectival '-shaped' construction.

Individually, 'saddle' originally meant a seat for a rider and 'shape' meant to form; together as 'saddle-shaped' the phrase came to mean 'having the shape of a saddle' and later was extended to technical senses (e.g., describing surfaces with opposing curvature in mathematics).