The invention relates to a rotary hydraulic machine which includes a casing (2) containing pistons actuated by an input shaft, said casing having a transverse front surface provided so as to engage with a mounting, and a transverse rear surface receiving a rear cover (4) supporting collectors connected to said pistons, the casing comprising side attachment tabs (30, 40) each having an axial bore (32) ending in a rear clamping surface, provided such as to receive an element for clamping said machine to the mounting, characterized in that at least one tab forms an axially elongate pad (40), the height of which is greater than half of the length of said casing included between the front and rear surfaces thereof.