Abstract: A shock absorbing frame assembly for a bicycle includes a coupling mount and a linking unit respectively disposed on the front and rear frame units and respectively having first and second gripping members. The first gripping member has two first jaws walls spaced apart along a first line. The second gripping member has two second jaw walls spaced apart along a second line that is in the same plane with the first line in a normal position. A twistable member includes left and right gripped regions in frictional engagement with the first and second gripping members, and an intermediate segment which is twistable to permit the second gripping member to turn to a strained position when the rear frame unit moves angularly relative to the front frame unit in response to a shock, and to acquire a biasing force to urge the second gripping member to the normal position to thereby counteract the shock.