An elastomer bush bearing, wherein the bearing body (2) is encapsulated through axial flanges (4, 4′) of the outer bearing sleeve (3), with the bush bearing having an elastomer bearing body (2) with a special profile in the axial direction. The bearing body (2) is employed in constructing the bush bearing of the invention, which is capable of supporting high radial loads even with low radial stiffness and without adversely affecting its stability and service life. The two axial end faces (5, 5′) of the bearing body (1) each have undulated contours which extend in the circumferential direction (u) in the same direction, both with respect to one another and also over the entire region of the material thickness (d) of the bearing body (2). The end faces (5, 5′) of the bearing body (2) thus have wave troughs (6, 6′, 7, 7′) and wave crests (8, 8′, 9, 9′), whereby the corresponding wave troughs (6, 6′, 7, 7′) of both end faces (5, 5′) and their wave crests (8, 8′, 9, 9′) are formed so as to face one another, and each extend radially over the entire material thickness (d) of the bearing body (2) in the respective circumferential segment.