We analyze the form of static charge susceptibility χ(q) in underdoped cuprates near axial momenta (Q,0) and (0,Q) at which short-range static charge order has been observed. We show that the momentum dependence of χ(q) is anisotropic, and the correlation length in the longitudinal direction is larger than in the transverse direction. We show that correlation lengths in both directions decrease once the system evolves into a superconductor, as a result of the competition between superconductivity and charge order. These results are in agreement with resonant x-ray scattering data [R. Comin, Science 347, 1335 (2015)SCIEAS0036-807510.1126/science.1258399]. We also argue that density and current components of the charge order parameter are affected differently by superconductivity: the charge density component is reduced less than the current component and hence extends deeper into the superconducting state. This gives rise to two distinct charge order transitions at zero temperature. © 2015 American Physical Society.