A shock absorber has dissipation power and practically no oil. The shock absorber comprising a rod-and-piston assembly slidable in a tubular body. The rod-and-piston assembly co-operating with the tubular body to define two working chambers containing hydraulic fluid. Each working chamber being in permanent communication with an auxiliary chamber containing a heterogeneous energy absorption-dissipation structure with at least one porous capillary matrix and an associated liquid relative to which the matrix is lyophobic. The two auxiliary chambers are annular chambers formed in the wall of the tubular body on either side of central portion of the tubular body. Each of the annular auxiliary chambers houses a flexible bag containing the associated heterogeneous structure; and each of the two working chambers also communicates with an associated compensation chamber. The compensation chambers ensures hydraulic fluid continuity during movements of the rod-and-piston assembly in the tubular body.