New light scalar degrees of freedom are motivated by the dark matter and dark energy problems. If coupled to matter, such scalars would mediate a fifth force. In order for the fifth force to be consistent with the present constraints, it must be suppressed close to the matter sources, through a non-linear screening mechanism. In this talk I will focus on a two-body problem in shift-symmetric theories that exhibit kinetic screening. The highly non-linear nature of the theory doesn't allow for an analytical solution away from spherical symmetry. I will present an approximate scheme that allows for a qualitative insight and in most of the parameter space very good quantitative agreement with the full numerical results. I will further discuss partial breakdown of the screening in such systems that could allow for further constraints of these theories.