This thesis presents an experimental and numerical study of the forces experienced by an object moving in granular media. This problem, which is of practical importance in many applications (robots, animal locomotion), is also of fundamental interest (rheology of granular materials, granular segregation). The experiment consists in a horizontal cylinder rotating around the vertical axis in glass beads. Both drag forces and lift forces experienced by the cylinder are measured. During the first half rotation, before the cylinder crosses its own wake, we measure a strong lift force (despite the symmetry of the object), about 20 times the buoyancy of the cylinder, and independent of its depth. Molecular dynamic simulations (Discrete Element Method) shed lights on how this lift force arises from the modification of the grain flow due to the pressure gradient in the medium. After several rotations, when the cylinder goes through its own wake, the drag force drops and becomes independent of depth. The rotation of the cylinder induces a structure in the granular packing, which screens the weight of the grains above it. Finally, a numerical study of forces on a large particle flowing with the granular medium is sketched, in relation with the phenomenon of granular segregation.