A vibrational energy absorbing apparatus 1 includes: a reciprocating member 2 which is reciprocatable in H directions between positive and negative maximum displacement positions D±max with respect to an origin position O; a damping-force generating means 3 for generating a damping force R with respect to the reciprocating motion of the reciprocating member 2 in the H directions; and a controlling means 4 for controlling the damping-force generating means 3 so as to cause the damping-force generating means 3 to generate a fixed damping force R in the respective movement of the reciprocating member 2 in the H direction from the positive and negative maximum displacement position D±max to the origin position O in the reciprocating motion thereof in the H directions, while causing the damping-force generating means 3 to substantially not generate the damping force R in the respective movement of the reciprocating member 2 in the H direction from the origin position O to the positive and negative maximum displacement position D±max following that movement in the H direction.