A device for the transosseous insertion of suture threads comprises:&mdasha main body (1), equipped with a grip (2), supporting a protruding cannula (3) provided with an active end (30)&mdasha flexible thread-like element (4) which is housed in a coaxially sliding manner inside the cannula (3) and is suitable, on command, for exiting from the active end (30) of the cannula (3). The thread-like element (4) is made of a super-elastic, shape-memory material and thus has the property of freely assuming, at least in an adequate temperature range for which its operative use is foreseen, a natural and predetermined curved form at least in a determined portion of the terminal part thereof. Means are provided for producing the coaxial movement of the thread-like element (4) in the two directions relative to the cannula (3).