A hydraulic shock absorbing apparatus for a vehicle includes a body left-side front wheel (7) (first traveling member) and a body right-side front wheel (8) (second traveling member), a left-side arm (11) (first connecting member) and a right-side arm (12) (second connecting member), and hydraulic shock absorbers (4, 5) provided between a vehicle body (3) and the left- and right-arms (11, 12). One end portion of each hydraulic shock absorber (4, 5) is formed by a cylinder main body (15) partitioned into a first oil chamber (21) and a second oil chamber (22) by a piston (23). The other end portion of the hydraulic shock absorber (4, 5) is formed by a piston rod (16) having the piston (23). The apparatus also includes a reserve tank (6) connected to one hydraulic shock absorber (4) via a first hydraulic oil passage (61) and connected to the other hydraulic shock absorber (5) via a second hydraulic oil passage (62). The first hydraulic oil passage (61) and the second hydraulic oil passage (62) are individually connected to a third oil chamber (57) of the reserve tank (6). It is possible to provide the hydraulic shock absorbing apparatus for the vehicle which can suppress a change in attitude of a vehicle body without increasing inclination of the vehicle body when the pair of hydraulic shock absorbers operate in the opposite directions while adopting an arrangement that can be readily manufactured.